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Results tagged with complex-geometry
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user 90655
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
votes
1
answer
406
views
Almost Complex manifolds of constant curvature
Edited (after R. Bryant comment)
Let $(M,\cal J,g)$ be a almost Hermitian manifold (not necessary integrable). i.e., ${\cal J}^2=-I$ and $g({\cal J} X,{\cal J} Y)=g(X,Y)$. Suppose that $\{X_i,{\cal J …
- 4,195
2
votes
1
answer
427
views
Is Thierry Aubin’s theorem true on Hermitian manifolds?
A classical theorem of Thierry Aubin states that:
Theorem (Aubin, T. 1979): If the Ricci curvature of a compact Riemannian manifold is
non-negative and positive at a point, then the manifold car …
- 4,195
2
votes
Contact and CR Examples
For a contact metric manifold $M$ we observe that $J = \varphi_{\vert D}$, i.e. the restriction
of $\varphi$ to the contact distribution, defines an almost complex structure on $D=\ker\eta$. Then the
…
- 4,195