Hermitian-Poisson Metrics on Flat Bundles over Complete Hermitian Manifolds

Abstract

In this paper, the author solves the Dirichlet problem for Hermitian-Poisson metric equation $\sqrt { - 1} {\Lambda _\omega }{G_H} = \lambda {\rm{Id}}$ and proves the existence of Hermitian-Poisson metrics on flat bundles over a class of complete Hermitian manifolds. When λ = 0, the Hermitian-Poisson metric is a Hermitian harmonic metric.

Keywords

Flat bundle / Hermitian harmonic metric / Hermitian-poisson metric / Complete Hermitian manifolds

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