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Results tagged with complex-geometry
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Complex geometry is the study of complex manifolds, complex algebraic varieties, complex analytic spaces, and, by extension, of almost complex structures. It is a part of differential geometry, algebraic geometry and analytic geometry.
9
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Accepted
Almost Complex Structure extending to Complex Structure, aka "Integrable"
A general type of question is if you have something that looks like a differential of something else, is it really the differential of something. If there is, we call the system integrable. If the man …
- 27.5k
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Weitzenböck Identities
I don't know of any precise definition of Weitzenbock identities, which is closely related to or also known as the Bochner technique. It is basically a way to write some invariantly defined second ord …
- 27.5k
1
vote
Accepted
about decomposition of three forms
I have no idea what the second half of the statement is, but here's what I think the first half says:
If $X \in V$ and $\theta \in V^*$ such that $\langle \theta, X\rangle \ne 0$, then given any nonz …
- 27.5k
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The Monge- Ampère equation with a non positive right hand side
In general nothing is known. Only local solvability is known for some special cases.
- 27.5k
0
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Which are the recommended books for an introductory study of complex manifolds?
I recommend having two or three books around. Sometimes you understand one book's explanation of a topic better than the others. I also found it helpful to read a book on Riemann surfaces, such as Gun …