Principal bundles on compact complex manifolds with trivial tangent bundle

Details Principal bundles on compact complex manifolds with trivial tangent bundle Principal bundles on compact complex manifolds with trivial tangent bundle

2011-04-06

arxiv.org/abs/1104.0996v1

Mathematics

Differential Geometry

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Scientific paper

Let $G$ be a connected complex Lie group and $\Gamma\subset G$ a cocompact lattice. Let $H$ be a complex Lie group. We prove that a holomorphic principal $H$-bundle $E_H$ over $G/\Gamma$ admits a holomorphic connection if and only if $E_H$ is invariant. If $G$ is simply connected, we show that a holomorphic principal $H$-bundle $E_H$ over $G/\Gamma$ admits a flat holomorphic connection if and only if $E_H$ is homogeneous.

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