Talk:Complex differential form

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Great job, SR!. Charles Matthews 12:44, 18 November 2005 (UTC)

A few things:

  • Sorry about the awkward sectioning. I (or someone) will fix it later. Furthermore, I know the intro to the Complex differential forms section is a bit redundant with the article intro. I imported this from differential form.
  • Thanks for pointing my in the right direction, Charles. I did a search for complex differential form, but got nothing. Speaking of which, complex differential form is probably a more appropriate title for the article.
  • Also, this article, including my own contributions, is prejudiced towards complex forms on complex manifolds. There are cases in which one may want to consider complexified forms where the underlying manifold does not carry a complex structure (e.g., CR manifolds.) Anyway, I'll see if I can find a way to remove this bias unobtrusively.

Best Regards, Silly rabbit 12:58, 18 November 2005 (UTC)

[edit] Stable

The article states:

By the Cauchy-Riemann equations, one can show that if we used a different holomorphic coordinate system wj, the spaces Ω1,0 and Ω0,1 are stable.

What does the word "stable" mean here? I can guess that maybe its a synonym for "invariant" or "complete". However "stable" also connotes the idea that its immune to small perturbations, and I don't think that that is what is meant. linas 23:13, 18 November 2005 (UTC)

Ok, after nearly eight months... My inclination is to leave the word stable. To be completely precise, one would have to say "stabilized under the biholomorphism group" which is sort of a mouthful. Invariant is not correct, since the spaces are not invariant. They are equivariant, but that opens a whole other can of worms. I've changed the sentence structure and added a bit of clarification. Let me know if it's okay. Thanks for pointing it out. Silly rabbit 21:26, 9 June 2006 (UTC)