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Results tagged with complex-geometry
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user 121820
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.
6
votes
Accepted
A closed $(1,1)$-form $\eta$ is harmonic if and only if $\Lambda\eta = \text{constant}$
Let $\eta$ be a closed $(1,1)$-form.
Then $\partial\eta=0$ and $\overline{\partial}\eta=0$.
Recall the Kähler identity
\begin{equation*}
[\partial,\Lambda] = -i\overline{\partial}^\ast .
\end{equatio …
- 1,713
6
votes
Accepted
$S^3$ as a Sasakian Manifold
I will answer your question for $S^{2n+1}$, since there is no difference between the case $n=1$ and the case of general $n$.
Let $(M^{2n+1},g,\theta)$ be a Sasakian manifold. One definition of a Sas …
- 1,713