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

IF 0.6 4区数学 Q3 MATHEMATICS

Differential Geometry and its Applications Pub Date : 2023-12-08 DOI:10.1016/j.difgeo.2023.102093

Indranil Biswas , Sorin Dumitrescu

引用次数: 0

Abstract

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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卡勒卡拉比尤流形上具有全态连接的主束

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。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Differential Geometry and its Applications 数学-数学

CiteScore

1.00

自引率

20.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Differential Geometry and its Applications publishes original research papers and survey papers in differential geometry and in all interdisciplinary areas in mathematics which use differential geometric methods and investigate geometrical structures. The following main areas are covered: differential equations on manifolds, global analysis, Lie groups, local and global differential geometry, the calculus of variations on manifolds, topology of manifolds, and mathematical physics.