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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.

1 vote
0 answers
231 views

every where levi flat

"Suppose $N$ is $2n-1; n\geq 2$ dimensional $CR$ manifold and everywhere Levi flat, then it will be locally $CR$ equivalent to $S^1\times \mathbb C^{n-1}.$" Above statement can be found in Loop sp …
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3 votes
1 answer
1k views

A corollary to Stone-Weierstrass theorem

Can i get the answer to the following problem. I am having a proof, i feel there is something wrong here..Can you please point out! Let $D\subset \mathbb C$ be a simply connected domain, and $\gamma …
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-1 votes
1 answer
92 views

Related to the Schwarz Christoffel map

With the help of the Schwarz-Christoffel map, for a given polygon (given angle), we can find some points on the boundary of the upper half plane, such that a particular Schwarz-Christoffel map takes t …
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2 votes
1 answer
259 views

What does non-levi flat point mean geometrically

Hello, $CR$ manifold for example $S^1\times C^{n-1}$ is every where levi flat. Can I have example of $CR$ manifold which has at least one non levi flat point. I can't see what the happening in Non …
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