Talk:G-structure on a manifold

Page title changes prior to the merge, as per the consensus above. Klbrain (talk) 08:33, 25 June 2016 (UTC)[reply]

The contents of the Reduction of the structure group page were merged into G-structure on a manifold on 25 June 2016. For the contribution history and old versions of the redirected page, please see its history; for the discussion at that location, see its talk page.

I'll leave the request for expert template above, as it is worth an expert looking at what was mostly a full-content merge to a new section. Klbrain (talk) 08:44, 25 June 2016 (UTC)[reply]

As a very inexperienced contributor to wikipedia, I am not sure how to proceed, but I am fairly sure that the merging of these two articles was not necessarily a good idea: the notion of "reduction of the structure group" is something that is defined for *any* principal bundle (and indeed, it is mentioned in the article on principal bundles), while a G-structure is a very specific kind of principal bundle (according to this article). Nielius (talk) 10:46, 20 July 2016 (UTC)[reply]

Merge cleanup proposal

It seems really necessary to me (mathematician working in a related field) to restructure this. I propose:

1. Move "Examples" and "Integrability" out of "Reduction of the structure group" (since they clearly apply to G-structures on manifolds, and not general bundles)
2. Rephrase "Reduction of the structure group" to make clear that it talks about general bundles
3. Move "Examples" further up
4. Bring a precise definition of G-structure before the examples, followed by a precise definition of "reduction of structure group"

If this is ok, I'll do it. --TurionTzukosson (talk) 10:29, 8 May 2018 (UTC)[reply]

I agree that a restructuring and clarification of concepts applicable to G-structures vs general bundles would would significantly improve this article. Your approach seems reasonable to me. Go for it. --Mark viking (talk) 16:43, 9 May 2018 (UTC)[reply]

The article in its present form gives a super short definition of G-structure (and a reference to the definition of principal G-subbundle is missing*). Then most of the discussion is about "Reduction of the structure group". This gives the impression that this is the same notion. However, the comment of Nielius in this talk page (20 July 2016) seems to hint that they are not. I highly recommend that there be a "Definition" section where the definition of G-structure is repeated and expanded a litte bit. If Wikipedia does not have a definition of the notion of principal G-subbundle it could be added here and to the article "Principal bundle".

(*): there is a ref to the artcile "Subbundle" but this is insufficient: a subbundle of a G-bundle is, I suppose, not a principal G-subbundle...

Arnaud Chéritat (talk) 13:07, 11 June 2022 (UTC)[reply]

Given its position in the article, the sentence "For a Lie group ${\displaystyle \displaystyle G}$ and a group homomorphism ${\displaystyle \displaystyle \phi \colon G\to GL(n)}$, a ${\displaystyle \displaystyle G}$-structure is a reduction of the structure group of the frame bundle to ${\displaystyle G}$." sounds like a property, buy I suspect this is intended to be the definition of G-structure. This should be clarified, and this definition should also appear at least in the header and I strongly suggest it also appears as the fist section of the article since the article is called "G-structure on a manifold". Arnaud Chéritat (talk) 08:44, 12 June 2022 (UTC)[reply]