Talk:Differential form

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[edit] Closed form redirect

I think that closed form should redirect here, rather than to de Rham cohomology as at present; and also should be disambiguated with respect to the 'closed form solution' meaning.

Charles Matthews 14:03, 11 Nov 2003 (UTC)

[edit] Disagree with merging closed and exact differential forms into here

See Talk:Closed and exact differential forms (unsigned comment by Oleg Alexandrov (talk))

[edit] symplectic form

Hi, sorry if this is a mixture or request/comment/question, but i was just wondering if symplectic differential form has any relation with this, and what exactly the correct definition would be. —The preceding unsigned comment was added by Evilbu (talk • contribs) .

Either a 2-form, or a closed 2-form - probably the latter, in contemporary literature. Charles Matthews 22:25, 6 February 2006 (UTC)
In addition to being closed, a symplectic form must also be nondegenerate. See symplectic manifold for details. There are words like almost-symplectic, which means not necessarily closed, etc. Orthografer 00:57, 3 November 2006 (UTC)

[edit] multilinear map from \wedge^n\ TM?

The article claims "At any point p on a manifold, a k-form gives a multilinear map from the k-th exterior power of the tangent space at p to R." Wouldn't this be just a linear map from the exterior power (which itself, however, might be thought of as a alternating multilinear map on TM\times\cdots\times TM)? Tesseran 05:59, 24 July 2006 (UTC)

We cannot consider a multilinear map on TM\times\cdots\times TM because this is not a linear space. Commentor (talk) 02:00, 27 March 2008 (UTC)

[edit] Why

you people don't explain why you use indexes below and above without any care? Why don't you explain that there is an advantage by indexing above for coordinated function? --kiddo 01:56, 2 November 2006 (UTC)

[edit] Page complexity

I think this page is too complex for general wikipedia users. Any one expert on this topic please make the page more comphrensive. —Preceding unsigned comment added by 76.184.2.133 (talk) 11:19, 18 October 2007 (UTC)

[edit] notation

Why is a basic 1-form written in two different ways in this article. Sometimes it's dx^i, sometimes it's dx^I? Randomblue (talk) 18:04, 2 February 2008 (UTC)

A form with capital indices is a k-form rather than a 1-form. This is explained in the article. Silly rabbit (talk) 18:12, 2 February 2008 (UTC)

When we integrate a function f over an m-dimensional subspace S of \mathbb{R}^n, we write it as

\int_S f\,{\mathrm d}x^1 \cdots {\mathrm d}x^m.

Consider dx1, ...,dxn for a moment as formal objects themselves

In the one case we go up to dx^m, and in the other dx^n. Is this an error? Randomblue (talk) 22:25, 2 March 2008 (UTC)

Yes, an error. It's so minor that I am not sure it's worth fixing it --- maybe somebody will be motivated by that to do some more substantial improvements :) 02:04, 27 March 2008 (UTC) —Preceding unsigned comment added by Commentor (talk • contribs)
But we are integrating here over S, not over Rn. S is a submanifold of dimension m. So one integrates m-forms over S, not n-forms. silly rabbit (talk) 02:20, 27 March 2008 (UTC)