This article may be true, but I don't recall this term being referenced, or defined. --Alan del Beccio 23:14, 14 April 2007 (UTC)
- "Riemannian tensor field" was referenced in "the vengeance factor". that was redirected here by the user who created this artciel. fyi. -- Sulfur 02:57, 15 April 2007 (UTC)
- If the episode only referenced Riemmanian tensor field, then there should at least be an article at that place. Granted, we don't know what it is and don't have much to write about that, but still there needs to be something there. --Jörg 07:54, 15 April 2007 (UTC)
- Well, I found the original reference in TNG: "The Vengeance Factor" - Scene 29:
- Wesley: It's the locally Euclidean metrization of a k-fold contravariant Riemannian tensor field.
- k-fold refers to a manifold which is usually locally Euclidean metrisised (so I don't know what's so special about it) and a Riemannian tensor field is nothing but a n × m "vector" field which is applied to a manifold. From a mathematicians' point of view Riemannian geometry should be a good header, because it does also catch the part of the k-(mani)fold. Of course just the tiny part of the R' tensor field was mentioned. -- Kobi 12:02, 15 April 2007 (UTC)
- In this case, k-fold refers to the type of tensor, and "fold" doesn't mean manifold, but the rank of the tensor, which is not actually an n × m "vector", but actually an nk vector or perhaps an n1 × n2 × ... × nk vector. Which is more or less irrelevant to the name of the article. Althai 23:06, 15 April 2007 (UTC)
- Well, I found the original reference in TNG: "The Vengeance Factor" - Scene 29:
- If the episode only referenced Riemmanian tensor field, then there should at least be an article at that place. Granted, we don't know what it is and don't have much to write about that, but still there needs to be something there. --Jörg 07:54, 15 April 2007 (UTC)
Merge
This article should've been moved to Riemannian tensor field, but instead someone created an article at that redirect. I am fairly sure that Riemannian geometry was not mentioned in "The Nth Degree," and we shouldn't have articles for concepts not mentioned. If a "Riemannian tensor field" is too trivial, then it might be placed under Geometry, however that's a different argument.--Tim Thomason 19:09, 15 April 2007 (UTC)
- But the concept is mentioned, and we do have articles for those that are inferred. Riemannian geometry is inferred, in this case, but the sum of the referenced components mentioned in the other subsection. --Alan del Beccio 22:56, 15 April 2007 (UTC)
- An object studied in Riemannian geometry was mentioned. While the actual reference was to "Riemannian tensor field" it seems silly to have an article on such an esoteric topic, since nobody is likely to care what a Riemannian tensor field is, beyond that it is a type of object which occurs in the mathematical field of Riemannian geometry. Furthermore, it is entirely possible that Riemannian geometry comes up in other episodes (I don't happen to know offhand) and is also important to general relativity, but the specific object mentioned by Wesley is unlikely to appear elsewhere. Also, Wikipedia will certainly have an article on Riemannian geometry in the 24th century, assuming it still exists, and will probably not have one on Riemannian tensor fields, so from the point of view that Memory Alpha is really an in-world encyclopedia, it makes more sense that the article be "Riemannian geometry". Personally, I would be in favor of a merge, with "Riemannian geometry" being the title of the merged page, and "Riemannian tensor field" being a redirect. Althai 23:00, 15 April 2007 (UTC)
==Tenses==
Why does someone keep changing everything to past tense? I stopped changing it to avoid an edit war, but it seems silly. The current version says Riemannian geometry "was a branch of mathematics in the 24th century", which gives the misleading impression that it was only in that century that it was a branch of mathematics.
In the real world, it was founded in the 19th century, continues to be a very important mathematical topic in the 21st century, is completely necessary to even describe General Relativity, and will almost certainly survive 10 centuries, just as Euclidean geometry has already survived over 20 centuries. Hence it should be in present tense. The "Geometry", "Pythagorean Theorem" and "General Relativity" pages are all written in the present tense, and Riemannian geometry seems no different. Althai 23:55, 15 April 2007 (UTC)