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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.

-2 votes
1 answer
1k views

holomorphic extension of a function [closed]

hi, I have the following question: let $U \subset \mathbb{C}^{n}$ be some open set containing zero. let $\tilde{U} = U \cap \mathbb{R}^{n}$. assume we have a real-valued analytic function $f : \tilde …
bruno's user avatar
  • 29
2 votes
1 answer
415 views

holomorphic extension of forms

hallo, I have the following question: Let $M$ be a $n-$dimensional complex manifold and $X \subset M$ be a compact $n-$dimensional totally real analytic Riemannian submanifold. Let furthermore $\alph …
bruno's user avatar
  • 29
1 vote
2 answers
605 views

Kähler manifold with Ricci-flat Kähler form

hallo, I have the following problem: Let $X$ be a $n-$dim Kähler manifold with Ricci-flat Kähler form $\omega$. There is a known fact that then there exists a holomorphic (n,0)-form $\Omega$ such tha …
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