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Talk:Riemannian manifold

Reorganization
I reorganized the page, added some things, and deleted others. I think it reads better now. I plan to add a section on curvature and the geodesic equation. I've left the very last section exactly as is since it doesn't naturally go into the other one, but it'll be subsumed into the eventual part on the geodesic equation.

Sorry if I changed too much or deleted something I shouldn't have. It seemed like some of the material was transplanted from books that obscured some of the point, and there was a lot of repetition and unclear statements. I tried to make sure that what I added is on a readable level.

Gumshoe2 (talk) 09:00, 3 May 2020 (UTC)

Restructuring to emphasize the case when the metric is smooth
Hi! Mathwriter2718 here. In the past few days I have made substantial modifications to this page. Most of my changes need no justification, but recently I have changed the page so that the metric is smooth (except for one section on the non-smooth case, which I am currently cleaning and shortening). I don't expect that this is controversial, but I want to justify it anyway.

A Riemannian manifold means that the metric is smooth. This is the default mathematical convention and other pages on Wikipedia invariably agree with this. It is very unusual for the word "Riemannian manifold" to mean that there is no regularity at all on the metric, as was previously the case on this page. In geometric analysis, one considers things that are "almost Riemannian manifolds", but the case when you just so happen to have an honest-to-goodness smooth manifold with an honest-to-goodness non-regular metric is a very special case that shouldn't be the default assumption on this page. More often, the "almost Riemannian manifolds" considered in geometric analysis aren't even smooth manifolds! Indeed, if you look at the main source for the content on the previous versions of this page about the non-smooth case (Gromov), you will see that the results this page cites from it are actually not about smooth manifolds with non-regular metrics, but about much weaker spaces. Mathwriter2718 (talk) 19:22, 25 June 2024 (UTC)

 * I agree that this article should focus on the case where the metric is smooth. Thanks for your work. Mgnbar (talk) 20:17, 25 June 2024 (UTC)
 * Thank you very much for these edits. Many of them are fixing some ill-advised edits (as I can see in hindsight) which I had made to the page back in 2020. I think the section on continuous metrics can be completely deleted; it can just be mentioned briefly in the metric space section (with reference to Bridson and Haefliger's book) that there is no modification required if the metric is only assumed to be continuous, or even Finsler. I may also try to rewrite that section a little to be a bit more direct, also removing the proof I had added; the Myers–Steenrod theorem should also be briefly discussed there.
 * Purely as a side note, Riemannian manifolds are indeed often taken to be smooth, but there are notable counterexamples, such as Bridson and Haefliger's textbook which takes them to be continuous, or Schoen-Yau on the positive mass theorem with a C5 metric. Gumshoe2 (talk) 22:57, 12 July 2024 (UTC)
 * Those are interesting counterexamples. I support having some light discussion of low regularity metrics on this page, but I think Finsler metrics and pseudo-Riemannian metrics are best discussed elsewhere. I think it makes sense to have the low regularity discussion be a few sentences sprinkled throughout the article where relevant instead of its own section. As far as I can tell, when working with continuous metrics, pretty much everything works exactly the same up until you get to connections, which falls flat on its face if the metric is not at least a few times differentiable. But I wouldn't trust my opinion on this without a second person backing this up. Mathwriter2718 (talk) 01:29, 15 July 2024 (UTC)

Why should I care?
Ok so I know Wikipedia math pages are famously mathy, but this important topic could use at a mention of where this thing is used and why. Johnjbarton (talk) 21:02, 4 July 2024 (UTC)

 * I believe physics is going to be the most rich source of applications. Mathwriter2718 (talk) 12:10, 5 July 2024 (UTC)
 * There are now many applications mentioned, but a section on applications is yet to be written. Mathwriter2718 (talk) 12:53, 16 July 2024 (UTC)

More modern stuff
It seems like this article could include links to more modern stuff. The Laplace–Beltrami operator, which is important in modern spectral theory of Riemannian manifolds. Einstein manifolds deserve a mention, and maybe Thurston geometrization. Kahler manifolds and connections to algebraic geometry. (Besse's Einstein manifolds in a good general source for a lot of this. I think Berger has a big survey book too.) Maybe the Yamabe problem too.

Also notably absent from the history is the Italian school (Bianchi, Ricci, etc), and the early contributions of Darboux, Monge, and others in the 19th century. Tito Omburo (talk) 22:03, 4 July 2024 (UTC)

 * I absolutely agree that the page would benefit from most of these things being added. When it comes to something like Kahler manifolds, I'm not sure where the line of things that really ought to have a drawn-out discussion on this page is drawn. But perhaps it should still be mentioned. Mathwriter2718 (talk) 12:07, 5 July 2024 (UTC)
 * Do you have a good reference for the history of the Italian school? Mathwriter2718 (talk) 12:54, 16 July 2024 (UTC)
 * If you can get it, the bibliography to Schouten's Ricci calculus lists dozens of relevant papers by Ricci and cohorts, especially Bianchi as well as others. Ricci developed what is nowadays called tensor calculus (in Riemnnian manifolds).  An amusing footnote on page 146 states that the Bianchi identity was originally discovered by Voss in 1880, independently rediscovered by Ricci and sent to Padova who published it in 1889, and then independently discovered a third time by Bianchi in 1902.  Tito Omburo (talk) 13:47, 16 July 2024 (UTC)

WikiProject Mathematics Discussion
There is a discussion concerning this article at Wikipedia_talk:WikiProject_Mathematics. Mathwriter2718 (talk) 11:54, 5 July 2024 (UTC)

A couple of example pictures, not sure if useful

I've selected these pictures possibly. Tito Omburo (talk) 15:41, 6 July 2024 (UTC)

 * I find the first one curiously unconvincing. The pentagon surrounding the foreground ('up close') has curved sides, but the one dead center ('further away') looks regular. Maybe the caption can guide the reader to particular comparisons? Johnjbarton (talk) 15:54, 6 July 2024 (UTC)

 * Good point. Is it fair to say that the polyhedra look more distorted (rather than just their polygonal faces)? Tito Omburo (talk) 17:59, 8 July 2024 (UTC)
 * Unfortunately is it difficult for me to pick out the polyhedra. Maybe this topic needs comparisons between Riemannian and Euclidean images? Johnjbarton (talk) 18:30, 8 July 2024 (UTC)

Here's maybe a better pairing? I've also updated the first caption to be a little more geometrical. Tito Omburo (talk) 21:07, 8 July 2024 (UTC)

 * I think the honeycomb pair is clear and effective.
 * I'm unsure what the torus is showing. In particular, the caption says a lot that is not in the image ("flat torus" in ordinary words is not a sensible combination) but omits critical aspects such as the meaning of the rotation. To me the caption requires too much background. Johnjbarton (talk) 23:31, 8 July 2024 (UTC)

Ok, a better version of the second image (not animated). Tito Omburo (talk) 00:13, 9 July 2024 (UTC)

 * I think captions should start with a description of the scene/object. If I ignore your description I would make up this caption (as someone who does not understand the topic):
 * A torus representing a 2D Riemannian manifold in a 3D Euclidean space. The Riemannian metric is not flat as can be seen by the unequal lengths of the bold lines. For many applications, a flat metric would be appropriate.
 * This may be completely off base, but perhaps it sets the level I think the caption should aim for. Johnjbarton (talk) 01:47, 9 July 2024 (UTC)
 * How about "A torus can be given a flat Riemannian metric, so that in the picture shown, the lengths of all heavy segments in the mesh are equal. Here a flat torus is embedded conformally (preserving angles) but not isometrically (preserving lengths) into Euclidean space." Tito Omburo (talk) 01:53, 9 July 2024 (UTC)
 * Better. The term "flat metric" is not defined in the article. The phrase "the lengths of all the heavy segments in the mesh are equal" keeps tripping me up. It is clearly not true in ordinary words. Johnjbarton (talk) 15:46, 9 July 2024 (UTC)

I'd hoped to make the point with one image, but here is a two image combo. Tito Omburo (talk) 21:16, 9 July 2024 (UTC)

 * The image on the left is an almost-square parallelogram, not a torus. I assume the text is implying the transformation shown in this image (from Torus) which would create a torus from the almost-square parallelogram?
 * Torus from rectangle.gif
 * Your final statement "Thus the intrinsic geometry of a flat torus is different from that of an embedded torus." seems to be what you are trying to show. I would expect to see two tori or perhaps one torus and an explanation for why the second one cannot be drawn.
 * I'm also not clear on the connection to the article topic. (By the way I'm trying to be helpful not annoying ;-) Johnjbarton (talk) 22:39, 9 July 2024 (UTC)
 * A torus is obtained from a (Euclidean) parallelogram by identifying opposite edges. This is for many applications the natural Riemannian structure on a torus. But it cannot be visualized in the usual way, by an embedding into Euclidean space.  The intrinsic geometries are different. Tito Omburo (talk) 23:26, 9 July 2024 (UTC)
 * I'm missing something key, perhaps the phrase "embedding into Euclidean space". You say:
 * A torus is obtained from a (Euclidean) parallelogram by identifying opposite edges. This is for many applications the natural Riemannian structure on a torus.
 * To me that is illustrated by the blue checkered pattern image.
 * But it cannot be visualized in the usual way, by an embedding into Euclidean space.
 * So "it" is not the blue checkered pattern image I guess? The orange one is clearly distorted. Why? I guess that the operations used to create the blue image are invalid so we must do something different and end up with the orange one. Johnjbarton (talk) 02:29, 10 July 2024 (UTC)
 * The blue image also illustrates this, provided one understands the initial rectangle as already a torus (after its opposite edges are identified). The process of realizing this torus in Euclidean space, however, involves strectching the sheet in ways that distort the metric.  Tito Omburo (talk) 09:47, 10 July 2024 (UTC)
 * I think the blue animation is the best bet, though I also really like the picture of the orange torus before and after identification. I think the blue animation's caption is much better for the lead and the orange torus's caption is better for the section on isometric embeddings. I would like to mention that there really is a $$C^1$$ isometric embedding of the flat torus into $$\mathbb R^3$$ which is visualized on the page Flat torus, though there is no $$C^2$$ isometric embedding of the flat torus into $$\mathbb R^3$$ (see https://www.emis.de/journals/em/images/pdf/em_24.pdf pages 7-9). Mathwriter2718 (talk) 12:38, 10 July 2024 (UTC)
 * Indeed, I made that image! But since we're explicitly in the smooth category, I think we can minimize the need to mention it. My original idea was an isometric embedding into the 3-sphere, stereographically projected into R^3, but this is too confusing I think. Tito Omburo (talk) 12:55, 10 July 2024 (UTC)
 * It's a very nice image!
 * I think the stereographic projection might be confusing, but I wonder what a bunch of cross-sections of the flat torus would look like.
 * I really like the idea of having a multiple image like what is shown on the right for the lead. (See the very long lead discussion at WikiProject_Mathematics.) I also like the idea of having the flat torus, the embedded torus, and an animation connecting the two all in a multiple image. (Of course here the aspect ratios and colors don't match up.) Specifically, I just think the animation would be enlightening for people who don't know how to transform the square with sides identified into the embedded torus.
 * What do you think about this? Mathwriter2718 (talk) 13:39, 10 July 2024 (UTC)
 * (I suggest taking a still image out of the blue gif rather than the orange square).
 * I guess the phrase "with sides identified" makes sense if you already understand the subject. Here is how I would rewrite the first sentence:
 * The Riemannian manifold called a flat torus (left) looks like a square when rendered in Euclidean space, but traveling to the right wraps around to the left and top to the bottom. Attempting to embedded it in Euclidean space (right) bends and stretches the square in a way that changes the geometry. Thus the intrinsic geometry of a flat torus is different from that of an embedded torus.
 * Johnjbarton (talk) 16:21, 10 July 2024 (UTC)
 * With a little extra work, the flat torus could be clarified by drawing on it some curves, such as a loop which passes over the would-be edges of the square, and noting that the lengths of these curves (and the angles between them) are exactly as they visually appear. This way it's possible to directly talk about the fundamental Riemannian notions of length and angle.
 * In that spirit, given a specific embedding of the side-identified square in R3, the difference in intrinsic geometry can be seen from the fact that the family of constant-y (or constant-x, depending on the embedding) loops on the square have nonconstant length once put through the embedding, while they clearly have constant length in the standard metric on the side-identified square. This isn't powerful enough to say that the induced metric isn't flat, but it's perfectly enough to say that what you're looking at is not an isometric embedding.
 * I don't think it is clear (either formally or intuitively) that the flat torus cannot be smoothly isometrically embedded. The simplest way I know to see this is by using the Theorema Egregium to say that the Gaussian curvature of the embedded torus is positive at a maximal-distance point from the origin. I think it is probably impossible to have a more elementary demonstration of this, given the C1 Nash–Kuiper embeddings (to which Theorema Egregium doesn't apply). It would be possible to say, at bare minimum, that a flat torus in R3 would have to possess a family of constant-length loops sweeping out the whole surface, orthogonal to anther family of constant-length loops sweeping out the surface. But this may not be significant enough to mention by itself, since I think it isn't obvious that even the standard embedding of the torus fails to satisfy this: it is only clear that the 'obvious' families of loops on the torus fail to satisfy this, only one of the two having constant length. Gumshoe2 (talk) 17:14, 10 July 2024 (UTC)
 * This was one consideration that led me to use a stereographic torus rather than a "standard" torus. Tito Omburo (talk) 17:24, 10 July 2024 (UTC)
 * This was one consideration that led me to use a stereographic torus rather than a "standard" torus. Tito Omburo (talk) 17:24, 10 July 2024 (UTC)

 * I think the illustration of hyperbolic space and the animation of the torus with stereographic projection of SU(2) look very cool, but are far too non-transparent in meaning to be used here. I'm not even personally sure what they mean. (What is "an observer" in hyperbolic space? Is it based on a use of the exponential map? And why is the torus moving?) Gumshoe2 (talk) 17:25, 10 July 2024 (UTC)
 * Yes, technically it is the preimage of the tessellation under the exponential map. I agree the animation is cool, and while it claims to be stereographic, the piecewise lines mesh is a bad illustration for this purpose. In case you didn't notice, I produced a better still of a stereographically projected torus with a smooth mesh. Tito Omburo (talk) 17:46, 10 July 2024 (UTC)

@Tito Omburo @Johnjbarton @Gumshoe2 I just updated the lead and in that update, I put in a version of the torus multiple image. Just wanted to say that I realize a consensus hasn't emerged here yet, and once a consensus reached, feel free to replace the multiple image I put in. Mathwriter2718 (talk) 02:30, 13 July 2024 (UTC)

 * @Tito Omburo @Johnjbarton @Gumshoe2 this conversation has dried up, but I don't think we ever came to a clear consensus. What image do you support using for the lead? Mathwriter2718 (talk) 12:52, 16 July 2024 (UTC)
 * In my view this topic was not focused on images for the lead, but on possible images and captions. I expected to see the tetrahedron tiling image as that one is convincing.
 * In the lead an image should ideally be solely about the topic. It should be the simplest or most iconic image related to the topic. I would go with something like the tangent-plane-on-sphere in the lead.
 * As I have discussed above, describing the torus images leads away from the topic, as far as I can tell. The purpose of an image is to give the reader an object to help connect the words of the article. When the words of the caption are confusing, the image disconnects the reader from the article. Showing a square then calling it a "flat torus" without this being discussed in the article has this effect on me. It signals to me that the article is not going to be helpful. Johnjbarton (talk) 16:07, 16 July 2024 (UTC)

How about this? Tito Omburo (talk) 16:58, 16 July 2024 (UTC)

 * LGTM Johnjbarton (talk) 17:05, 16 July 2024 (UTC)

Bold definitions
@Dedhert.Jr you recently changed a few bolded definitions on this page to be italicized instead. I am reverting this edit for two reasons: Mathwriter2718 (talk) 01:43, 8 July 2024 (UTC)
 * 1) I am not aware of any style guide saying that definitions on math articles are supposed to be italics and not bold. I didn't see anything on Manual_of_Style/Mathematics about this.
 * 2) You left the vast majority of definitions bolded, and I don't see any difference between the definitions you unbolded and the ones you left bolded.

 * @Mathwriter2718. This is explained in MOS:NOTBOLD: "Avoid using boldface for introducing new terms. Instead, italics are preferred". Dedhert.Jr (talk) 04:40, 8 July 2024 (UTC)
 * @Dedhert.Jr I see, thanks. I have redone your edit changing the definitions to italics but I have applied it to all of the definitions outside of the lead. Mathwriter2718 (talk) 12:08, 8 July 2024 (UTC)

Distance metric confusion.
I complained about this sentence when it was in the lead; now it is the body: However, the Definition section of the article confuses Riemannian metric and "distance" in the normal sense of the word: Furthermore a main section of the article is "Metric space structure", implying to a reader that a Reimannian manifold is a "metric space" and the distance function is discussed several times in the article. In my opinion the Riemannian metric is to be confused with the distance function of a metric space, according to the article itself. It seems that the Riemannian metric is a kind of generalization of a distance metric but of course I don't know. The sentence is not sourced so I cannot look further into this issue. In my opinion this connection is important as it tells the non-math major about the relationship between this new thing in the article and a more familiar thing, "distance". Johnjbarton (talk) 16:59, 13 July 2024 (UTC)
 * A Riemannian metric is not to be confused with the distance function of a metric space, which is also called a metric.
 * A Riemannian metric puts a measuring stick on every tangent space.

 * I agree that there is confusion here. The situation is the following (just for talk page purposes I will use "metricS" to refer to a metric in the sense of a metric space, and "metric" to refer to a Riemannian metric). A metric defines a metricS (via a somewhat complicated procedure), and in this sense a Riemannian manifold "is" a metric space (among other things). However most metricS's do not correspond to any metric, and so most metric spaces do not correspond to any Riemannian manifold. Notably the metricS corresponding to a given metric fully characterizes the original metric due to the Myers-Steenrod theorem, in the sense that if two metrics are given and their corresponding metricS's are isometric ('the same') in the sense of metric spaces, then the two metrics are isometric ('the same') in the sense of Riemannian manifolds. For this reason, often the word "metric" (and "isometry") in the Riemannian-geometric context does indeed have a somewhat blurred meaning, with (because of Myers-Steenrod) there being little danger involved.
 * In other words, one could say that Riemannian manifolds form a (small) subclass of metric spaces, but nonetheless a metric is a very distinguishable object from the corresponding metricS: one is a collection of inner products and the other is a real-valued function with point-pair input. Sometimes if the word "metric" is used in Riemannian geometry you have to infer from context whether the metric or corresponding metricS is meant; in practice this is usually easy. "Riemannian distance function" refers unambiguously to the metricS.
 * In the end I think the page should communicate the above in some way. Gumshoe2 (talk) 17:26, 13 July 2024 (UTC)

 * Strictly speaking, Riemannian manifolds are only metric spaces when they are connected (presumably Riemannian manifolds are automatically paracompact). It seems like something more along the lines of "integration of the metric allows one to define a distance function under which (connected) Riemannian manifolds become metric spaces." (and a link to where this is done in more detail in the article) Tito Omburo (talk) 18:21, 13 July 2024 (UTC)
 * Agreed, although I don't think paracompactness is relevant to this. (But at least in the sources I am familiar with, it's always taken as part of the definition of "manifold.") Gumshoe2 (talk) 18:30, 13 July 2024 (UTC)
 * I'm fine with manifolds being always paracompact. (I've seen claims that you get paracompactness for free if it's Riemannian, but I am skeptical.  Happy to be convinced either way.)  Tito Omburo (talk) 18:40, 13 July 2024 (UTC)
 * Every metric space is paracompact, so it comes down to whether or not you believe that paracompactness is needed to get a metric space from a continuous Riemannian metric. It seems to me that it's not; if so, then paracompactness is equivalent to existence of a continuous Riemannian metric. Gumshoe2 (talk) 18:49, 13 July 2024 (UTC)
 * You can make a disconnected Riemannian manifold a metric space by making each component a metric space via a silly procedure. This should be in Lee's Riemannian Manifolds. Mathwriter2718 (talk) 14:39, 14 July 2024 (UTC)
 * Worth noting that you need to assume that manifolds only have countably many components (which comes for free if you make the standard assumption that manifolds are second countable). Mathwriter2718 (talk) 15:16, 14 July 2024 (UTC)
 * I didn't see it in Lee, but I guess you could give a disconnected Riemannian manifold by picking basepoints on connected components and giving the set of basepoints the discrete metric. Tito Omburo (talk) 15:49, 14 July 2024 (UTC)
 * In general the disjoint union of metric spaces is a metrizable topological space, but without any particular metric which is natural. (In the standard approach you would modify by truncation the metrics on the individual connected components.) So if you have a Riemannian manifold, without assuming connectedness or paracompactness, you do still get paracompactness for free – since metrizable spaces are paracompact. Then second-countability comes out also if you assume there are countably many components. Gumshoe2 (talk) 18:13, 14 July 2024 (UTC)
 * My issue is that points in a non-paracompact space might not be joined by a smooth curve, although perhaps this is unfounded. Tito Omburo (talk) 19:31, 14 July 2024 (UTC)
 * Let M be a smooth manifold, not required to be paracompact or connected, with a Riemannian metric. Each connected component is a connected Riemannian manifold, not necessarily paracompact. Any topological space which is connected and locally path-connected is path-connected.
 * Take as given a continuous path $$[0,1]\to M$$; you need $$0=x_0<x_1<\cdots<x_k=1$$ such that the restriction of the path to each $$[x_i,x_{i+1}]$$ is contained in a coordinate chart; if you have this then you can immediately make a path with the same endpoints which is piecewise-smooth. (And then if you want this could be made smooth by rounding off corners.) This seems to be rather annoying but possible to get, based on starting with an open cover $$U_\alpha$$ of the interval for which the image of each $$U_\alpha$$ is contained in a coordinate chart; see here for instance.
 * So each connected component is smoothly path-connected. Then, using the Riemannian metric, each connected component is metrizable, and so M itself is metrizable and hence paracompact. Gumshoe2 (talk) 20:10, 14 July 2024 (UTC)
 * While we're on the subject, I ran into an annoying issue when writing about the distance function for this page. Lee's Riemannian Manifolds uses piecewise regular curves (which he calls admissible) in the definition of the Riemannian distance function. However, many papers in the field simply use piecewise smooth curves. You can prove these different definitions both yield the same Riemannian distance function, and I know the proof, but I can't find a reference for it, and of course citing original research is not allowed. Mathwriter2718 (talk) 23:50, 14 July 2024 (UTC)

Redlink
The redlink Constant scalar curvature metric seems like an important topic for which there should be an article or section, but the only sections that I could find were for restricted contexts. Is there somewhere appropriate to point it? -- Shmuel (Seymour J.) Metz Username:Chatul (talk) 07:56, 14 July 2024 (UTC)

 * This links to Yamabe problem. It strikes me that constant sectional curvature metrics (space forms) could also be mentioned.  Tito Omburo (talk) 10:40, 14 July 2024 (UTC)
 * I think csck metrics where most attention goes right now (as opposed to csc metrics), so I support using csck metrics as the example. Mathwriter2718 (talk) 13:57, 14 July 2024 (UTC)
 * @Gumshoe2 should be pinged on this. Mathwriter2718 (talk) 15:03, 14 July 2024 (UTC)
 * I changed the link from constant scalar curvature Kähler metrics (cscK) to Yamabe problem for two separate reasons:
 * in context the sentence is
 * ...many special metrics such as constant scalar curvature metrics and Kähler–Einstein metrics are constructed intrinsically using tools from partial differential equations.
 * Stylistically, I think the Kähler–Einstein problem is too close to the cscK problem for these to both be usefully mentioned/linked next to each other. (The cscK problem is a generalization of the Kähler–Einstein problem, worked on by the same research community and largely with the same techniques.) I think there should be more variety.
 * There are very many Kähler–Einstein metrics found by PDE techniques which are genuinely new, previously unknown, examples of Riemannian manifolds. There is a large variety of them, inaccessible by other methods, and their existence theory is basically resolved (Calabi conjecture and Yau-Tian-Donaldson conjecture). In contrast, although everyone expects that there should be even more cscK metrics found by similar techniques, as far as I know this is still almost entirely conjectural. So I think it is actually a little inappropriate to mention them here separately as examples of Riemannian manifolds; at this point in time, most known examples of cscK metrics are just the Kähler–Einstein metrics.
 * By the way, in the near future I plan to add a short section to the body of the article on these Riemannian metrics constructed by analytic means. Gumshoe2 (talk) 18:37, 14 July 2024 (UTC)
 * Sounds fair enough to me. Mathwriter2718 (talk) 23:19, 14 July 2024 (UTC)
 * Space forms should undoubtedly be discussed on the page and possibly also in the lead, but as a separate class of examples not to do with PDE. Gumshoe2 (talk) 18:39, 14 July 2024 (UTC)

Lie groups, homogeneous spaces, and symmetric spaces
@Gumshoe2 thank you for adding your new excellently-written sections on Lie groups, homogeneous spaces, and symmetric spaces. However, I am concerned with how early in the article they are: they reference geodesic completeness, the Riemann and Ricci curvature tensors, scalar curvature, and the Levi-Civita connection, and more, all before those terms have been discussed. What do you think about putting them all under a new section directly under the section about connections, geodesics, and curvature? Also, I hope you won't mind if I change the inline math to be in LaTeX for consistency with the rest of the article. Mathwriter2718 (talk) 00:00, 15 July 2024 (UTC)

 * I strongly prefer to avoid tags whenever possible, since in some browsers (including my own) the horizontal rendering for it is very distracting.
 * I think it would make sense to move the whole Examples section to right before the 'infinite dimensions' section. At present the first four example sections don't require any advanced material, so it would be ok to split them out and keep those four where they are now, but in the end I think they should contain some commentary to do with curvature and geodesics – especially the one on submanifolds. So my preference is to move them as you suggest, but keeping them all together — but I don't feel so strongly about it, you can reorganize however you think best. Gumshoe2 (talk) 00:21, 15 July 2024 (UTC)
 * Let's leave the issue of tags vs templates on this page unresolved for now, and I will just not change anything.
 * It is necessary to introduce many examples early on, but then they should be discussed again in more details later. I'm not sure what the best way to do this is, but I can imagine several possible ways to do it, including a) having two sections about examples, one defining them, and a later one discussing them all again, b) having two sections about examples, one basic examples, one more advanced examples, c) discussing a few examples as each new concept is introduced.
 * For now, I made your space forms subsection its own section and put the Lie groups, homogeneous spaces, and symmetric spaces subsection into a new section titled (maybe poorly) "Lie groups". Arguably, all four could also go under one heading that would be something like "Especially symmetrical Riemannian manifolds".
 * Mathwriter2718 (talk) 01:20, 15 July 2024 (UTC)
 * I changed the titling a bit but I think this is a good fix for now. I think your suggestions in #2 are good (perhaps 2b the most?); as some more content is added we can think more about the best way to organize it.
 * There's also the issue of what should go here and what should go instead in Riemannian geometry. I have essentially no sense of the difference between these pages; should any of the content presently on this page go there? Gumshoe2 (talk) 03:46, 15 July 2024 (UTC)
 * Based on absolutely nothing, I decided that Riemannian geometry is about the subject, its history, and big theorems and conjectures, and Riemannian manifold is about specifically the structure of a Riemannian manifold, basic theorems, the objects you can put on Riemannian manifolds, related structures, and examples. I myself haven't touched Riemannian geometry at all. Mathwriter2718 (talk) 04:11, 15 July 2024 (UTC)
 * Is that to say that there's nothing in particular on either page that you think should be moved to the other? Gumshoe2 (talk) 04:14, 15 July 2024 (UTC)
 * I don't have a strong opinion, but I think it looks fine. Mathwriter2718 (talk) 11:54, 15 July 2024 (UTC)

title: Talk:Riemannian manifold


text:
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Alex was trained by his father Steve Wright, a British professional wrestler. He wrestled his first match in 1991 in Germany when he was sixteen years old. He wrestled in his hometown during his early career and also worked in Japan.

Das Wunderkind (1994–1996)
Wright was discovered by World Championship Wrestling (WCW) in mid-1994 when WCW toured through Germany. He signed a contract with Time Warner, the parent company of WCW, and went through more training at the WCW Power Plant. Wright made his WCW debut, defeating Brady Boone on the September 3rd edition of Saturday Night. He originally wrestled as a babyface and was known as "Das Wunderkind" Alex Wright. His entrance music ("Warped Mind" by Dominic Glynn), was of the techno genre, which was popular in some American and German dance clubs at the time, and he often danced as he walked to the ring or once he got in the ring. His first feud was with Jean-Paul Levesque, whom he defeated at Starrcade in December in both men's pay-per-view debut. In his early career, Wright went undefeated in matches against several WCW superstars including Bobby Eaton in January 1995 at Clash of the Champions XXX and Paul Roma at SuperBrawl V in February '95. However, the latter saw Roma's contract later terminated by WCW because of his stiff performance and his disregard of instructions to put Wright over during the match. WCW had Wright feud on and off with Disco Inferno, another wrestler who danced in or on his way to the ring, with Wright representing modern dancing and music, and Disco representing older styles. Wright would win all of the matches in this feud.

Wright wrestled Arn Anderson for the WCW World Television Championship on an episode of WCW Saturday Night and beat Anderson by DQ. A rematch was scheduled for the next pay-per-view, Slamboree, where Wright suffered his first loss.

Due to WCW's partnership with New Japan Pro-Wrestling (NJPW), Wright participated in NJPW's Best of the Super Juniors and finished third in the tournament. He started wrestling against fellow cruiserweight and babyface Brian Pillman, whom he defeated in the opening match at The Great American Bash. On the July 16 edition of Main Event before Bash at the Beach, Wright teamed with Marcus Bagwell to face Dick Slater and Bunkhouse Buck in a losing effort. He had encounters with other up and coming WCW stars such as Diamond Dallas Page in August at Clash of the Champions XXXI. In September 1995 on Nitro, Wright wrestled Sabu. Sabu won the match but continued to attack Wright, even putting him through a table. Referee Nick Patrick thus reversed his decision, disqualifying Sabu for his violence and giving the win to Wright. Wright had several matches against Eddie Guerrero, with a very notable match taking place on The Main Event before Fall Brawl 1995: War Games, which resulted in a draw. Wright also had several matches in '95 and '96 against Dean Malenko. In January 1996, at Clash of the Champions XXXII, Malenko defeated Wright by pinfall.

At World War 3, Wright took part in the first-ever three-ring 60-man battle royal for the vacant World Heavyweight Championship, which was won by Randy Savage. At Starrcade, WCW wrestlers faced NJPW wrestlers in a World Cup of Wrestling. Wright represented WCW against NJPW's Koji Kanemoto (for the IWGP Junior Heavyweight Championship even though WCW never announced it as such) but ended up losing the bout to Kanemoto. Wright then began a feud with Dick Slater, to whom he lost at Uncensored in a singles dark match. At Slamboree, Wright was forced by WCW to be teamed with his wrestling and dancing nemesis Disco Inferno in a tag team match against Slater and Eaton. Wright and Disco lost when Disco was pinned. In June of '96, famed Japanese wrestler Antonio Inoki helped put together the World Wrestling Peace Festival, which was held in Los Angeles. Wright wrestled and lost to Chris Benoit on that card. On the August 10 edition of Saturday Night that aired immediately before Hog Wild, Wright defeated Bobby Eaton in a rematch.

At World War 3, Wright again participated in a three-ring, 60-man battle royal, with the winner getting a shot at the World Heavyweight Championship. The battle royal was won by The Giant. In January '97 on Clash of the Champions XXXIV, Wright lost to Masa Chono, who had recently come to the U.S. and joined the nWo.

Championship reigns (1997)
WCW had Wright wrestle in several tag team matches with fellow midcarders, mostly on the losing side. On the May 12, 1997, edition of Nitro, Wright partnered with Ice Train against Konan and Hugh Morrus of the Dungeon of Doom, a match in which Wright openly displayed heelish behavior such as teasing the return of his dance routine that he had temporarily shelved as a babyface, and clashing with Train's manager Teddy Long during the match. This culminated in Wright claiming to be unable to continue due to a sudden unexplainable knee injury, angrily confronting Long and then abandoning Ice Train, leaving him to lose the match by submission. Wright was then pushed as a heel for the remainder of 1997, which led to his first championship gold: on the July 28 edition of Nitro, he defeated Chris Jericho to win the Cruiserweight Championship. Wright feuded with Jericho thereafter, including a successful title defense against Jericho at Road Wild, before dropping the title back to Jericho on August 16 edition of Saturday Night. However, five days later, he defeated Último Dragón on the August 21 Clash of the Champions XXXV to win the World Television Championship. Wright was able to successfully defend the TV title against Lord Steven Regal on an episode on Nitro.

At Fall Brawl, Wright made a successful title defense against Último Dragón in a rematch before dropping the title to rival Disco Inferno on September 22 edition of Nitro. Wright feuded with Steve McMichael after McMichael's valet Debra left him and became Wright's valet. She ordered the feud and in the rivalry, Wright defeated McMichael at Halloween Havoc, with help from Goldberg, who promptly attacked Wright postmatch. The next month at World War 3, McMichael took out Goldberg prior to their match and Wright was literally dragged to the ring by Debra to wrestle McMichael again, and this time suffered a defeat.

Wright would go on to be managed by Debra for a little while longer. Debra would often try to illegally interfere in matches to help him win, but the plan would usually backfire, causing Wright to lose. He then cut ties with Debra after a string of losses that Wright claimed was her fault.

The Dancing Fools (1998)
Wright would then begin to patch things up with former rival Disco Inferno as they began teaming in 1998 to form a moderately successful tag team called the Dancing Fools, which at times also featured Japanese wrestler Tokyo Magnum in the role of a tag-along who regularly attempted to imitate their dancing styles. Wright and Inferno feuded with The Public Enemy (Johnny Grunge and Rocco Rock), including a loss to Grunge and Rocco at Road Wild. Wright then began an angle where he claimed that he was the best WCW wrestler to come out of Europe. British Bulldog, however, disputed Wright's proclamation, leading to a feud between Wright and Inferno against Bulldog and Jim Neidhart. The feud culminated at Fall Brawl, where the Dancing Fools lost to Bulldog and Neidhart. After suffering losses, Wright and Inferno split and began singles careers again.

Wright feuded with another fellow European wrestler, Fit Finlay, because he blamed Finlay for ending his father's career. Wright took his father's revenge from Finlay by beating him at Halloween Havoc.

Wright again competed in the 60-man battle royal at the '98 edition of World War III, with that year's battle royal being won by Kevin Nash.

Berlyn (1999–2000)
At the beginning of 1999, Wright was kept off WCW television for an extended length of time until May, when Wright came up with his own idea for a gimmick. Promotional spots began appearing on WCW television featuring Wright as a surprising new Rivethead-style character named Berlyn (an intentional misspelling of the city Berlin, the capital of Wright's home country Germany), with a black Mohawk and goatee replacing his blond hair. He was clad entirely in black with a long trench coat and arrogantly refused to speak English. He spoke through an interpreter—Uta Ludendorff—and was accompanied to the ring by a large wrestler known as The Wall. The promos coincided with the aftermath of the Columbine school massacre, which threw a hitch in WCW's plans. Sensing the unintentional similarities in dress between Berlyn and the teenage killers, WCW delayed the debut of Berlyn for several months. During his debut on August 30 on Nitro, he quickly insulted Americans, debuting the character as a heel.

Wright was booked to face Buff Bagwell at Fall Brawl shortly after his debut, but the match did not take place. While WCW claimed that Bagwell had missed his flight, Bagwell was in the arena but did not want to lose. WCW replaced Bagwell with Hacksaw Jim Duggan, and Wright's problems continued as Duggan no-sold all of Wright's offense and did not cooperate in the ring. Berlyn instead wrestled and defeated Bagwell on the next night's Nitro. Afterwards, Berlyn attacked Scott Armstrong and began a feud with Brad Armstrong. Alex (as Berlyn) and Brad Armstrong had a match at Halloween Havoc, which Berlyn lost. After the match, Berlyn and The Wall attacked Armstrong. Although Berlyn had been given a push after the fiasco with Duggan and Bagwell, his gimmick was unpopular. WCW furthered the damage by giving The Wall a singles push, leaving Wright to flounder in the mid-card.

On the October 25 edition of Nitro, it was announced that a tournament would be held for the vacant World Heavyweight Championship and the finals would occur at Mayhem. On the following edition of Nitro, Berlyn participated in the tournament but lost his first round match to Vampiro. Berlyn began a small feud with Vampiro and cost him his second round match in the tournament against Buff Bagwell. At Mayhem, Vampiro defeated Berlyn in a Dog Collar match after the Wall turned on Berlyn. Berlyn then feuded with the Wall before again disappearing from WCW television again.

Boogie Knights (2000–2001)
After several months off from wrestling, Wright returned under his real name on the September 27, 2000, edition of Thunder during a match between former partner, Disco Inferno, now renamed "Disqo" (a pun on the name of then-popular R&B singer Sisqó), and Konnan. Wright helped Disqo in getting the victory and the duo reunited as the Boogie Knights. Wright was now completely bald but had returned to his previous dancing mannerisms. The Boogie Knights began a feud with The Filthy Animals while they also feuded with two members of The Natural Born Thrillers (Sean O'Haire and Mark Jindrak), who were the World Tag Team Champions at the time. At Halloween Havoc, the three teams participated in a triangle match but O'Haire and Jindrak won the match. Disqo and Wright would then go on to win the World Tag Team Championship from O'Haire and Jindrak at Millennium Germany on November 16. However, four days later on Nitro, due to Disqo being out with an injury, Wright and substitute Elix Skipper lost the titles to Chuck Palumbo and Shawn Stasiak, two other members of the Natural Born Thrillers.

Wright then started an angle where he kept KroniK (Brian Adams and Bryan Clark) as his bodyguards to squash other cruiserweights. At Mayhem, Wright and KroniK faced Billy Kidman and Rey Misterio, Jr. in a 3-on-2 handicap match. However, KroniK abandoned Wright after the 15 minutes they were paid for expired, leading to him being pinned. Disqo eventually returned from his injury and the Boogie Knights gimmick lasted until WCW was purchased by World Wrestling Federation (WWF) in March 2001. Wright remained under contract with AOL Time Warner, as his contract was not bought out by the WWF.

Retirement
Wright fell out of the spotlight after the folding of WCW and has not appeared on American television since then. Wright stated in an interview that WWE could not sign him as he was one of the few who was under contract with AOL Time Warner at the time. He also stated that he took a break from wrestling as he was not happy with the backstage politics in WCW that were happening at the time. In the years following, Wright has stayed away from regular active competition, only wrestling on rare occasions for German wrestling promotions NAWA and GWP.

He wrestled his last match on May 31, 2003 defeating Chris the Bambi Killer for NAWA in Uelzen, Germany.

After working as a banker and fitness instructor, he opened a pro-wrestling school called "The Wright Stuff" in Nuremberg, Germany. Notable students include current WWE wrestler Giovanni Vinci. In 2009, he started his own wrestling promotion called New European Championship Wrestling (NEW).

Championships and accomplishments

 * Pro Wrestling Illustrated
 * Rookie of the Year (1995)
 * Ranked No. 54 of the 500 best singles wrestlers of the year in the PWI 500 in 1995
 * Ranked No. 408 of the top 500 singles wrestlers of the PWI Years in 2003
 * World Championship Wrestling
 * WCW Cruiserweight Championship (1 time)
 * WCW World Television Championship (1 time)
 * WCW World Tag Team Championship (1 time) – with Disco Inferno
 * World Cup Of Wrestling (1995) – with Sting, Randy Savage, Lex Luger, Johnny B. Badd, Eddie Guerrero, and Chris Benoit

Other media
Wright appears in the wrestling themed episode of Louis Theroux's Weird Weekends. In this episode, Wright mentions that he was to debut his new gimmick (Alexander Wright) that night in WCW. He later renamed the gimmick "Berlyn".

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Alex Wright


text:
User:Zh

''Man is born free but everywhere is in chains. — Jean-Jacques Rousseau''

My interests:

 * Fly fishing
 * Mandolin

title: User:Zh


text:
Bethany College

Bethany College may refer to:

Australia

 * Bethany College (Sydney), New South Wales

Canada

 * Bethany Bible College, New Brunswick
 * Bethany College (Saskatchewan)

United States

 * Bethany College (Kansas), Lindsborg, Kansas
 * Bethany College (West Virginia)
 * Bethany Global University, Bloomington, Minnesota
 * Bethany Lutheran College, Mankato, Minnesota
 * Bethany Lutheran Theological Seminary, Mankato, Minnesota
 * Bethany Theological Seminary, Richmond, Indiana
 * Bethany University, Scotts Valley, California, formerly known as Bethany Bible College and Bethany College
 * College of the Sisters of Bethany, Topeka, Kansas

title: Bethany College


text:
Category talk:Nuclear weapons

There's a bit of a problem with this being in the "weapons of mass destruction" category: there are nuclear weapons like the dirty bomb and smaller-scale tactical warheads which aren't so-called WMDs. I have no idea of a more appropriate category for this to be in, nor can I think of a good immediate solution. So it's really just something to think about. -Lommer 05:42, 16 Jul 2004 (UTC)
 * I think that dirty bombs and tactical warheads are considered WMDs in many contexts, even if a dirty bomb doesn't cause that much "destruction" per se. I think that any nuclear warheads -- tactical are not -- are considered WMDs, though they ride that line. The smallest nukes in the US arsenal are still more powerful than the bomb used to attack federal building in Oklahoma City, for example -- even things that are a "mere" kiloton or so are pretty destructive. In any event, I don't think it matters all that much... --Fastfission 00:13, 17 Jul 2004 (UTC)

title: Category talk:Nuclear weapons


text:
Privilege (law)

A privilege is a certain entitlement to immunity granted by the state or another authority to a restricted group, either by birth or on a conditional basis. Land-titles and taxi medallions are examples of transferable privilege – they can be revoked in certain circumstances. In modern democratic states, a privilege is conditional and granted only after birth. By contrast, a right is an inherent, irrevocable entitlement held by all citizens or all human beings from the moment of birth. Various examples of old common law privilege still exist – to title deeds, for example. Etymologically, a privilege (privilegium) means a "private law", or rule relating to a specific individual or institution.

The principles of conduct that members of the legal profession observe in their practice are called legal ethics.

Boniface's abbey of Fulda, to cite an early and prominent example, was granted privilegium, setting the abbot in direct contact with the pope, bypassing the jurisdiction of the local bishop.

One of the objectives of the French Revolution was the abolition of privilege. This meant the removal of separate laws for different social classes (nobility, clergy, and ordinary people), instead subjecting everyone to the same common law. Such privileges were abolished by the National Constituent Assembly on August 4, 1789.

title: Privilege (law)


text:
Talk:Flag of the Australian Capital Territory

Designer?
I find the article incomplete without the mention of the name of the designer. Caeruleancentaur (talk) 12:08, 6 December 2010 (UTC)

History and adoption
I have prepared some information about the history of the flag and its adoption, including the retrieval of a survey form from the 1993 public survey process. I would be grateful for any improvements, suggestions or questions from others that might help to improve this section.

Additionally, owing to the inexact use of "Coat of arms of the ACT" in this article (and indeed, in the article on the coat of arms of the city of Canberra) I have amended the references to such throughout. Gtlloyd (talk) 07:35, 5 July 2021 (UTC)

Distinction between city emblems and territory emblems
I have today reversed a few changes made recently by an anonymous user that changes specific references that changed certain references to 'city of Canberra' emblems to the 'Australian Capital Territory' emblems. A number of persistent efforts seem to be afoot to change references to "city of Canberra" to "Australian Capital Territory" in this article and the article on the Coat of Arms of the City of Canberra - even going so far as to amend the title of archival documents.

 * Coat of arms of the city of Canberra: Granted by royal warrant on 8 October 1928, with supporters added on 7 November 1928 when the city was granted the coat of arms. Confusingly, despite quite specific law on this subject, Wikipedia's article houses this coat of arms in an incorrectly titled article. Sources: https://www.pmc.gov.au/publications/australian-symbols-booklet/state-and-territory-symbols/symbols-australian-capital ; https://www.cmtedd.act.gov.au/communication/flags

 * Coat of arms of the Australian Capital Territory: Does not exist. There is a community reference group helping to develop designs for this emblem. The parliament held an inquiry in 2019 into whether it should create a coat of arms. Sources: https://yoursayconversations.act.gov.au/territory-emblems ; https://www.parliament.act.gov.au/__data/assets/pdf_file/0019/1405216/9th-ETCS-09-Inquiry-into-a-Territory-Coat-of-Arms.pdf ; https://www.pmc.gov.au/publications/australian-symbols-booklet/state-and-territory-symbols/symbols-australian-capital

 * Flag of Canberra: A maroon flag with the Canberra city coat of arms on it. Never seen nowadays, though some are in the local museum. Created by the Federal Capital Commission in 1929 and used unofficially as a territory flag in the absence of a Territory flag. Sources: https://www.crwflags.com/fotw/flags/au-act.html#form ; http://www.flagsaustralia.com.au/35%20Canberra.pdf

 * Flag of the Australian Capital Territory: This is the official flag of the Territory, but not of the city. It has, however, the coat of arms of the city on it.

Because Canberra is far and away that biggest settlement in the ACT, it might seem pedantic to distinguish between the two. However, as there may soon be an official Territory coat of arms, it's worth ensuring accurate terminology is used. There is also an accuracy issue, as many of the historical documents establishing the coat of arms refer explicitly to the city of Canberra, and edits to these references may make the original sources difficult or impossible to find.

The articles may also be the venue of politicking, as the inquiry received a number of submissions from pro- and anti- monarchists given elements of the Canberra city coat of arms reflect the Australian monarchy (notably, the crowns, portcullis white rose, and the motto). Gtlloyd (talk) 09:19, 11 April 2023 (UTC)


text:
Kikuyu Central Association

The Kikuyu Central Association (KCA), led by James Beauttah and Joseph Kang'ethe, was a political organisation in colonial Kenya formed in 1924 to act on behalf of the Gĩkũyũ community by presenting their concerns to the British government. One of its greatest grievances was the expropriation of the most productive land by British settlers from African farmers. Most members of the organisation were from the Gĩkũyũ tribe.

KCA was formed after the colonial government banned the earlier Young Kikuyu Association founded by Harry Thuku and the East African Association. In either 1925 or early 1926, Beauttah moved to Uganda, although remained in contact with Kenyatta. When the KCA wrote to Beauttah and asked him to travel to London as their representative, he declined but recommended that Kenyatta who had a good command of the English language go in his place. Kenyatta accepted, probably on the condition that the Association matched his pre-existing wage. He thus became the group's secretary. Jomo Kenyatta, later the first president of Kenya, joined it to become its General Secretary in 1927.

The Kikuyu Central Association was banned in 1940 when World War II reached East Africa. Some fighters of the later Mau-Mau still understood their struggle as a continuation of KCA and even called themselves KCA.

The end of World War II, however, saw the new type of African organisation that went beyond tribal boundaries with the rise of the Kenya African Union that later became KANU. Reasons for formation of KCA: 1)return of African Land 2)abolition of Kipande system 3)release of Harry Thuku 4)provision of quality education 5)end forced labour

KCA published the Muiguithania ("the reconciler"), a Kikuyu language newspaper. It was banned alongside KCA in 1940.

title: Kikuyu Central Association


text:
User talk:Twinxor

Template:InuyashaCharacter
Actually, saving some typing is only a useful side benefit to the Inuyasha character template. My main purpose in creating it was to ensure a uniform intro to all the character pages. Before I made it, I noticed that the character pages all had different variants of "[Name] is a character in InuYasha..." Creating a template is an easy way to ensure that they are all the same. In addition, it can be changed easily. [[User:JoshG|Josh | Talk]] 04:08, Sep 23, 2004 (UTC)
 * I don't see why it hurts to have different intros, as long as they're coherent. Anyway, someone listed it on Templates for deletion, and you may want to go defend it there. --Twinxor 04:21, 23 Sep 2004 (UTC)

PCB Milling/ PCB Prototyping topics
Hi,

For the record I'm the copyright holder (writer of) of **all** material on PCBprototyping.com, including graphics - I also own the site (registered under my company name: ximetrix systems). I'm happy to share the info here as I feel wikipedia a great concept. So - what's the next step to re-listing the topics? I also have several more to add...

Regards,

Ian Campbell ian@ximetrix.ca

 * I left a response on your user page. --Twinxor 04:52, 2 Oct 2004 (UTC)

Poli-substub
Hi Twinxor... Just noticed your creation (last month) of poli-substub. There's a general feeling at WikiProject Stub sorting that Category:Substubs shouldn't be divided into subcategories, and it's generally discouraged. The reason is that it means that twice the number of categories have to be sorted by editors to look for items to expand. In general, the substubs should be either expanded slightly and given the full stub subcategory (in this case poli-stub) or dealt with in other ways (vfd or merger). In cases where the article deserves to be kept, simply giving the article the stub subcategory is usually considered ok (since there's often not a lot of difference between a stub and a substub in those cases, and it will put the article somewhere where someone is more likely to expand it anyway). Basically, then, the general idea is no substub subcategories; use the stub subcategories instead. Grutness|hello? 10:12, 24 Mar 2005 (UTC)
 * Oops. I see now you simply amended the category... sorry! Grutness|hello? [[Image:Grutness.jpg|25px|]]

Thanks for message
Replying about message left about copyright tag on image:Kitkat, I will do. Should I do this for the other pictures i have ' fairused '!? Thanks again.

--Electricmoose 14:39, 28 Mar 2005 (UTC)

Octopus card photo
I didn't change it. See. --JuntungWu 14:49, 12 May 2005 (UTC)
 * That's true. Sorry for the confusion. --Twinxor 21:43, 12 May 2005 (UTC)

Dark and stormy night
You're quite welcome! It was one of those light and calm afternoons when I click on "randompage" and just edit whatever comes up! Nice article, I always laugh when I read the full first line of the novel. Happy editing, and hello from a Cal grad, Antandrus (talk)  21:54, 15 May 2005 (UTC)

Your edits to Template:Cycling stub
Regarding your recent edit to Template:Cycling stub : Please be careful not to delete the HTML tags or the link to Category:Cycling stubs because it screwed up all the articles that had this tag. Thanks. Zzyzx11 (Talk) 21:30, 2 Jun 2005 (UTC)
 * That was dumb, sorry. Twinxor t

sxc.hu images on the commons
Hi, I believe that a decision has been taken to the effect that sxc.hu images are OK on the commons if the uploader does not place additional restrictions on them. Thanks for letting me know that Image:firearms.jpg had been put on the deletion page, though. Lupin 15:23, 3 Jun 2005 (UTC)

Dave Kelly (Artist)
Why did you remove the sentence on "mixed marriages"? --KSnortum 08:30, 27 February 2006 (UTC)
 * It was unnecessary editorializing. Wikipedia is not the the place to make ironic comments pointing out peoples' closed-mindedness. Twinxor t 08:32, 27 February 2006 (UTC)
 * Good enough, I'll remove it again. Next time, would you at least put something in the discussion page about it?  It helps me to be a better editor to understand another person's reasoning than to just see a sentence disappear "for no reason".
 * [Edit] Ah, I see you did. Never mind. --KSnortum 01:43, 28 February 2006 (UTC)

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Hi. I don't think Nagorno-Karabakh War is up to the standart of a good article. It is written mostly from Armenian POV without any significant input of Azeri users. I did not attach the disputed tag, because I think it can be improved up to the required standart, but you can check the talk page and see that it has seriuos issues. So for the moment I recomend to remove nomination. Regards, Grandmaster 06:51, 28 June 2006 (UTC)

 * Yes, it is. It just needs input of Azeri editors, currently it reflects more the view of the Armenian side. I'm currently busy with Nagorno-Karabakh page, but I will contribute to this one as well. I think it can make it as a good article, it just needs more work. Take care. Grandmaster 07:24, 28 June 2006 (UTC)

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A new WikiProject. In case you're interested. - User:Samsara (talk • contribs) 17:30, 27 July 2006 (UTC)
 * Yeah, why not. Thanks for the heads-up. Twinxor t 18:13, 27 July 2006 (UTC)

Ubuntu thanks
To User:Localzuk, User:Twinxor, User:Easyas12c

Just wanted to say well done for your contributions to Ubuntu (Linux distribution), which were important in getting it to FA status, and for being involved on its FA day and/or the aftermath. It's always so much better working with a group of people towards a common goal than walking the walk alone. - User:Samsara (talk • contribs) 13:39, 6 August 2006 (UTC)

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Do you know the guy, or just know of him? Just curious. Cheers, Postdlf 03:23, 7 October 2006 (UTC)
 * I don't know him -- I just noticed a similar photo on one of the sites linked in the article. Twinxor t 02:14, 11 October 2006 (UTC)

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It seems more likely than not that the Eve Online example was put in by a malicious party and it could very well be biased. However, given that it is a specific example of something mentioned in the article and, given what I know about Something Awful, quite possibly true, it seems prudent to keep it in for the time being, at least long enough to give its creator time to find citations. I like your decision: keep in the barebones stuff and ask for verification, while taking out inflammatory material unless it can be cited, and I hope you would agree that it would look very bad for an article with SA's history of contention to have well-writen negative content consistently deleted. Stilgar135 18:23, 30 October 2006 (UTC)
 * I'm willing to look at a citation claiming that SA members engaged in such behavior, but I imagine that one isn't forthcoming and wouldn't be very credible. Again, I think you did the right thing, but if someone wants to make the argument, I'll listen to it (for only a second, most likely). Stilgar135 18:36, 30 October 2006 (UTC)

References added for Finland Plot article
Thank you very much for your suggestion on the Finland Plot article. I have added several references to back up the statements made in the Background section. I hope that you will have the time to review the edits, and if possible, judge whether the article is now worthy of Good Article status. Cheers, Patiwat 06:07, 4 November 2006 (UTC)
 * Thanks for your response. I've done as suggested, and also some other minor edits. Patiwat 21:56, 4 November 2006 (UTC)
 * Thanks for the pass! Patiwat 20:27, 5 November 2006 (UTC)

GA Hold
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Linux project
The Linux wikiproject exists. The articles in question are relevant to the wikiproject and should therefore be tagged as such. Kari Hazzard ( T  |  C ) 16:44, 11 November 2006 (UTC)

GA discussion
i've responded to your comments over at Talk:Kohlberg%27s_stages_of_moral_development. JoeSmack Talk 06:36, 1 December 2006 (UTC)

List of recordings preserved in the United States National Recording Registry
You are one of several people who was instrumental in cleaning up my List of recordings preserved in the United States National Recording Registry page. This page was the first page I created and still remains the page that I have made the most edits to on wikipedia (95 edits). Thank you for your assistance. Since this page received so much more cleanup assistance than most of my other pages I am wondering if it was a focus article of a WikiProject Group. Do you know of any such designation? It would be helpful because I will be self nominating for admin tomorrow or Tuesday. Please reply at my userpage with any info you may have. TonyTheTiger 17:23, 10 December 2006 (UTC)

Anti-Mac
Thanks for getting the deletion process going. --Ronz 16:40, 20 December 2006 (UTC)

Specialized Bicycle Components
Clean revisions undeleted. You could have simply asked. - crz crztalk 21:40, 2 January 2007 (UTC)

Recordings preserved in the National Recording Registry
You have contributed as an editor to the List of recordings preserved in the United States National Recording Registry. It is undergoing an overhaul according to the recent peer review that generated the following feedback. In addition to the changes there, it is undergoing stylistic changes that prevail at lists that have been selected as featured lists. Conversion to wikitable format began with 2002 today because most articles that reach featured list status are in this format. Feel free to convert additional years, add more columns, or add further details. Hopefully many of the editors who have helped edit this page to its pre review state will help improve it to a featured list quality level. I may not return to make further edits until next week. TonyTheTiger 21:02, 18 January 2007 (UTC)

Mountain Biking on Mount Tamalpais
Hello, An article that I created, Mountain Biking on Mount Tamalpais, has been listed for deletion. If you are interested in the deletion discussion, please participate by adding your comments at Articles for deletion/Mountain Biking on Mount Tamalpais. Thank you, Bob in Vegas - uriel8   (talk)  09:17, 17 February 2007 (UTC)

July 2007 GAC backlog elimination drive
A new elimination drive of the backlog at Good article candidates  will take place from the month of July through August 12, 2007. There are currently about 130 articles that need to be reviewed right now. If you are interested in helping with the drive, then please visit Good article candidates backlog elimination drive and record the articles that you have reviewed. Awards will be given based on the number of reviews completed. Since the potential amount of reviewers may significantly increase, please make sure to add :GAReview underneath the article you are reviewing to ensure that only one person is reviewing each article. Additionally, the GA criteria may have been modified since your last review, so look over the criteria again to help you to determine if a candidate is GA-worthy. If you have any questions about this drive or the review process, leave a message on the drive's talk page. Please help to eradicate the backlog to cut down on the waiting time for articles to be reviewed.

You have received this message either due to your membership with WikiProject: Good Articles and/or your inclusion on the Good article candidates/List of reviewers. --Nehrams2020 23:46, 10 July 2007 (UTC)

WikiProject Good Articles Newsletter for November 2007
The November 2007 issue of the WikiProject Good Articles newsletter has been published. Comments are welcome on this, as well as suggestions or offers of assistance for the December 2007 issue. Dr. Cash 01:24, 1 November 2007 (UTC)

WikiProject Good Articles Newsletter for December 2007
The December 2007 issue of the WikiProject Good Articles newsletter has been published. Comments are welcome on this, as well as suggestions or offers of assistance for the January 2008 issue. Dr. Cash 01:14, 4 December 2007 (UTC)

WikiProject Good Articles January Newsletter
Happy New Year! Here is the latest edition of the WikiProject GA Newsletter! Dr. Cash (talk) 04:09, 3 January 2008 (UTC)

WikiProject Good Articles Newsletter
The February 2008 issue of the WikiProject Good Articles Newsletter is ready! Dr. Cash (talk) 05:15, 1 February 2008 (UTC)

Disputed fair use rationale for Image:Incubation cover.jpg
Thanks for uploading Image:Incubation cover.jpg. However, there is a concern that the rationale you have provided for using this image under "fair use" may be invalid. Please read the instructions at Non-free content carefully, then go to the image description page and clarify why you think the image qualifies for fair use. Using one of the templates at Fair use rationale guideline is an easy way to ensure that your image is in compliance with Wikipedia policy, but remember that you must complete the template. Do not simply insert a blank template on an image page.

If it is determined that the image does not qualify under fair use, it will be deleted within a couple of days according to our criteria for speedy deletion. If you have any questions please ask them at the media copyright questions page. Thank you.BetacommandBot (talk) 23:37, 13 February 2008 (UTC)

Disputed fair use rationale for Image:Incubation screenshot.jpg
Thanks for uploading Image:Incubation screenshot.jpg. However, there is a concern that the rationale you have provided for using this image under "fair use" may be invalid. Please read the instructions at Non-free content carefully, then go to the image description page and clarify why you think the image qualifies for fair use. Using one of the templates at Fair use rationale guideline is an easy way to ensure that your image is in compliance with Wikipedia policy, but remember that you must complete the template. Do not simply insert a blank template on an image page.

If it is determined that the image does not qualify under fair use, it will be deleted within a couple of days according to our criteria for speedy deletion. If you have any questions please ask them at the media copyright questions page. Thank you.BetacommandBot (talk) 23:37, 13 February 2008 (UTC)

WikiProject Good Articles Newsletter
The March 2008 issue of the WikiProject Good Articles Newsletter is ready! Dr. Cash (talk) 06:14, 3 March 2008 (UTC)

April GA Newsletter
The April issue of the WikiProject Good Articles Newsletter is now available. Dr. Cash (talk) 04:06, 7 April 2008 (UTC)

WikiProject Good Articles May Newsletter
The May Newsletter for WikiProject Good Articles has now been published. Dr. Cash (talk) 22:16, 2 May 2008 (UTC)

WikiProject Good articles newsletter
Delivered by the automated Giggabot (stop!) 02:24, 9 June 2008 (UTC)

WikiProject Good Articles Newsletter
Sorry about the delay. AWB has been having a few issues lately. Here is the august issue of the WikiProject Good Articles Newsletter! Dr. Cash (talk) 20:56, 19 August 2008 (UTC)

WikiProject Good Articles Newsletter
Sorry about the delay. AWB has been having a few issues lately. Here is the august issue of the WikiProject Good Articles Newsletter! Dr. Cash (talk) 20:57, 19 August 2008 (UTC)

GA Sweeps invitation
Hello, I hope you are doing well. I am sending you this message since you are a member of the GA WikiProject. I would like to invite you to consider helping with the GA sweeps process. Sweeps helps to ensure that the oldest GAs still meet the criteria, and improve the quality of GAs overall. Unfortunately, last month only two articles were reviewed. This is definitely a low point after our peak at the beginning of the process when 163 articles were reviewed in September 2007. After nearly two years, the running total has just passed the 50% mark. In order to expediate the reviewing, several changes have been made to the process. A new worklist has been created, detailing which articles are left to review. All exempt and previously reviewed articles have already been removed from the list. Instead of reviewing by topic, you can consider picking and choosing whichever articles interest you.

We are always looking for new members to assist with the remaining articles, so if you are interested or know of anybody that can assist, please visit the GA sweeps page. In addition, for every member that reviews 100 articles or has a significant impact on the process, s/he will get an award when they reach that threshold. If only 14 editors achieve this feat starting now, we would be done with Sweeps! Of course, having more people reviewing less articles would be better for all involved, so please consider asking others to help out. Feel free to stop by and only review a few articles, something's better than nothing! Take a look at the list, and see what articles interest you. Let's work to complete Sweeps so that efforts can be fully focused on the backlog at GAN. If you have any questions about the process, reviewing, or need help with a particular article, please contact me or OhanaUnited and we'll be happy to help. --Happy editing! Nehrams2020 (talk • contrib) 08:51, 8 May 2009 (UTC)

April 2010 GAN backlog elimination drive
–MuZemike delivered by MuZebot 18:22, 25 March 2010 (UTC)

Revision to Sid Meier's Alien Crossfire and Sid Meier's Alpha Centauri articles
I noticed that you have revised either Sid Meier's Alpha Centauri or Sid Meier's Alien Crossfire.

I intend to revise those articles following the WikiProject Video games/Article guidelines. There are more details on the discussion pages of those articles. I'd be interested in any comments you have. It would be best if your comments were on the discussion pages of the two articles.

Thank you.

Vyeh (talk) 17:30, 6 June 2010 (UTC)

ArbCom elections are now open!
Hi, You appear to be eligible to vote in the current Arbitration Committee election. The Arbitration Committee is the panel of editors responsible for conducting the Wikipedia arbitration process. It has the authority to enact binding solutions for disputes between editors, primarily related to serious behavioural issues that the community has been unable to resolve. This includes the ability to impose site bans, topic bans, editing restrictions, and other measures needed to maintain our editing environment. The arbitration policy describes the Committee's roles and responsibilities in greater detail. If you wish to participate, you are welcome to review the candidates' statements and submit your choices on the voting page. For the Election committee, MediaWiki message delivery (talk) 22:17, 30 November 2015 (UTC)

"Haim Romano" listed at Redirects for discussion
An editor has identified a potential problem with the redirect Haim Romano and has thus listed it for discussion. This discussion will occur at Redirects for discussion/Log/2022 August 18 until a consensus is reached, and anyone, including you, is welcome to contribute to the discussion. signed,Rosguill talk 17:37, 18 August 2022 (UTC)

title: User talk:Twinxor


text:
Matos

Matos or Mattos may refer to:

Places

 * Salir de Matos, a parish in the municipality of Caldas da Rainha, Portugal
 * Matos River, a river in Bolivia
 * Matos Costa, a municipality in the Brazilian state of Santa Catarina

Other uses

 * Matos (surname), a Portuguese surname
 * Matoš, a Croatian surname
 * Matot or matos or (Hebrew מטות), the 42nd weekly parshah in the cycle of Torah reading
 * Matorral or mato, the scrublands, or heaths, of Portugal

title: Matos