Relative connections on principal bundles and relative equivariant structures

Mainak Poddar,Anoop Singh

doi:10.1016/j.difgeo.2023.102041

Relative connections on principal bundles and relative equivariant structures

Mainak Poddar, Anoop Singh

https://doi.org/10.1016/j.difgeo.2023.102041

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Journal: Differential Geometry and its Applications

Publication Date: Jun 28, 2023

Affiliation: Indian Institute of Science Education and Research Pune, Indian Institute of Technology BHU, Tata Institute of Fundamental Research

#Family Of Compact Complex Manifolds #Principal Bundle + Show 8 more

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Abstract

We investigate relative holomorphic connections on a principal bundle over a family of compact complex manifolds. A sufficient condition is given for the existence of a relative holomorphic connection on a holomorphic principal bundle over a complex analytic family. We also introduce the notion of relative equivariant bundles and establish its relation with relative holomorphic connections on principal bundles.

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