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Results tagged with kahler-manifolds
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user 124888
Questions about Kähler manifolds and Kähler metrics.
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Why are holomorphic $p$-forms parallel?
Let $X$ be a complex compact Kähler manifold, $\Omega_X$ its cotangent bundle and $D$ the Chern connection.
It is, I believe, a standard fact that parallel $k$-forms $\alpha \in \mathcal{A}^k(X)$, i.e …
- 175
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Global sections appearing in Dolbeault complex with values in vector bundle
Given a holomorphic vector bundle $E$ on a compact complex Kähler manifold $X$ (I am happy to assume $X$ projective), we can compute the sheaf cohomology $H^\ast(E)$ of $E$ using the Dolbeault complex …
- 175