卡勒卡拉比尤流形上具有全态连接的主束

Pub Date : 2023-12-08 DOI:10.1016/j.difgeo.2023.102093

Indranil Biswas , Sorin Dumitrescu

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引用次数: 0

摘要

我们证明，在紧凑的凯勒卡拉比优流形上，任何容许全形连接的全形向量束也容许平全形连接。这解决了阿蒂亚所提问题的一个特殊情况，并推广了之前在[6]中针对简单连接的紧凑凯勒卡拉比优流形得到的结果。我们给出了它在 Kähler Calabi-Yau 流形上的 Cartan 几何图形和叶状 Cartan 几何图形框架中的一些应用。

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

We prove that any holomorphic vector bundle admitting a holomorphic connection, over a compact Kähler 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 [6] for simply connected compact Kähler Calabi-Yau manifolds. We give some applications of it in the framework of Cartan geometries and foliated Cartan geometries on Kähler Calabi-Yau manifolds.

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