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arXiv · 1109.5808

Hermitian-Einstein connections on principal bundles over flat affine manifolds

Indranil Biswas·John Loftin
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Abstract

Let $M$ be a compact connected special flat affine manifold without boundary equipped with a Gauduchon metric $g$ and a covariant constant volume form. Let $G$ be either a connected reductive complex linear algebraic group or the real locus of a split real form of a complex reductive group. We prove that a flat principal $G$-bundle $E_G$ over $M$ admits a Hermitian-Einstein structure if and only if $E_G$ is polystable. A polystable flat principal $G$--bundle over $M$ admits a unique Hermitian-Einstein connection. We also prove the existence and uniqueness of a Harder-Narasimhan filtration for flat vector bundles over $M$.

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Indranil Biswas, John Loftin. 2011-09-27. Hermitian-Einstein connections on principal bundles over flat affine manifolds. https://arxiv.org/abs/1109.5808

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