Talk:Distribution (differential geometry)

Generalized distributions

I added the section on generalized distributions, but perhaps this should be a separate page. Does anyone know a good reference apart from the original papers of Stefan and Sussmann? Simplifix (talk) 11:45, 29 August 2008 (UTC)[reply]

Name

If this distribution has nothing to do with the usual mathematical sense of distribution, then why the name? Cesiumfrog (talk) 10:43, 13 August 2011 (UTC)[reply]

There are many senses of the word “distribution” in mathematics. The distributions in this article here have nothing to do with the better known ones from probability theory and functional analysis. 2800:200:E840:356E:C75:C5F:D434:A5F1 (talk) 03:53, 29 August 2022 (UTC)[reply]

Imprecise definition?

The article says that the vector fields $X_{1},\ldots ,X_{k}$ form a local basis for a distribution $\Delta \subset TM$ on an open $U\subset M$ if the vectors $X_{1}(p),\dots ,X_{k}(p)$ span $\Delta _{p}$ for every $p\in U$ . Is this standard terminology? This seems strange to me, because $X_{1}(p),\dots ,X_{k}(p)$ are not required to be linearly independent, but elsewhere in linear algebra a basis is required to be linearly independent. I would call $X_{1},\dots ,X_{k}$ a “local generating set” or something like that.

If $\Delta$ has a bona fide local basis around each point $p\in M$ , then $\Delta$ is actually a vector subbundle of $TM$ . Of course, every vector subbundle of $TM$ is a distribution, but the converse is not true. 2800:200:E840:356E:C75:C5F:D434:A5F1 (talk) 04:11, 29 August 2022 (UTC)[reply]

I adjusted the wording to resolve this. 67.198.37.16 (talk) 19:07, 29 May 2024 (UTC)[reply]

"of course"

seriously? a wikipedia entry about mathematics that says "of course" twice? is this a journal paper or wikipedia? 151.100.59.194 (talk) 11:27, 10 November 2023 (UTC)[reply]

Point taken. I'll remove it. (It's supposed to be obvious, if you understood the rest of what the text said.) 67.198.37.16 (talk) 18:42, 29 May 2024 (UTC)[reply]