Talk:Kähler manifold

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Mathematics rating:	Start Class	Mid Priority	Field: Geometry
Please update this rating as the article progresses, or if the rating is inaccurate. Click to show/hide comments. Please add to or update the comments to suggest improvements to the article. --Cronholm144 21:18, 15 June 2007 (UTC)

Kähler manifolds are usually thought of as finite dimensional manifolds. There is a generalized theory of infinite dimensional manifold, but it would be good to give at least one reference to literature dealing primarily with finite dimensional Kähler manifold. Hottiger 17:26, 6 March 2006 (UTC)

[edit] Why are they important?

I think this entry would benefit if the importance of Kahler manifolds is explained. I don't know it.

I second this comment. Kähler manifolds need to be motivated. LTX2mny (talk) 10:55, 22 April 2008 (UTC)

[edit] Definition

Many sources define Kahler manifolds as symplectic manifolds with integrable compatible almost complex structures. The relation between this definition and the definition via Kahler metrics should be made explicit. I would be tempted to give the definition mentioned here first in the article, and then later mention the relation with Kahler metrics. Of course, being a symplectic geometer I may be biased. What do other thinks? 136.152.180.51 23:23, 19 April 2007 (UTC)