Hermitian-Poisson metrics on projectively flat complex vector bundles over non-compact Gauduchon manifolds

TL;DR

This paper explores the existence of Hermitian-Poisson metrics on projectively flat complex vector bundles over non-compact Gauduchon manifolds, establishing a link with semi-simplicity using heat flow and continuity methods.

Contribution

It introduces a novel approach connecting Hermitian-Poisson metrics with semi-simplicity on such bundles via heat flow techniques.

Findings

Established a correspondence between Hermitian-Poisson metrics and semi-simplicity.

Applied heat flow and continuity methods to non-compact Gauduchon manifolds.

Abstract

In this paper, we investigate the projectively flat bundles over a class of non-compact Gauduchon manifolds. By combining heat flow techniques and continuity methods, we establish a correspondence between the existence of Hermitian-Poisson metrics and the semi-simplicity property on projectively flat bundles.