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Results tagged with complex-geometry
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user 14515
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.
4
votes
Are compact, complex, affinely flat manifolds geodesically complete?
This is an answer to the last question of the revised version of your question which is
"What if instead of the the parallel almost complex structure we assume that there is a nonzero parallel vecto …
- 4,787
8
votes
Are compact, complex, affinely flat manifolds geodesically complete?
Let me give a standard example of a closed incomplete manifold with flat affine structure, whose 2-dimensional version is essentially the example from the comment of Misha.
Consider $R^n\setminus 0$ …
- 4,787
15
votes
Accepted
Alternative Almost Complex Structures
Let us first deal with linear algebra. Assume a matrix $J$ satisfies $J^k= -Id$.
Then, there exists a poylnomial $P$ whose coefficients depend on the eigenvalues of your $J$ such that
$P(J)$ is a …
- 4,787
3
votes
Accepted
Are there hermitian metrics with the volume form of a Kahler metric?
A property of a hermitian metric to be conformally Kähler is a very restrictive property and a generic hermitian metric is not conformally Kähler.
The property of the volume form to be equal to so …
- 4,787