Principal bundles with holomorphic connections over a Kaehler Calabi-Yau manifold

Indranil Biswas; Sorin Dumitrescu

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arXiv · 2312.01399

Principal bundles with holomorphic connections over a Kaehler Calabi-Yau manifold

Indranil Biswas·Sorin Dumitrescu

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Abstract

We prove that any holomorphic vector bundle admitting a holomorphic connection, over a compact K\"ahler Calabi-Yau manifold, also admits a flat holomorphic connection. This addresses a particular case of a question asked by Atiyah and generalizes a result previously obtained in \cite{BD} for simply connected compact K\"ahler Calabi-Yau manifolds. We give some applications of it in the framework of Cartan geometries and foliated Cartan geometries on K\"ahler Calabi-Yau manifolds.

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Indranil Biswas, Sorin Dumitrescu. 2023-12-03. Principal bundles with holomorphic connections over a Kaehler Calabi-Yau manifold. https://arxiv.org/abs/2312.01399

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