Hermitian-Poisson Metrics on Flat Bundles over Complete Hermitian Manifolds

In this paper,the author solves the Dirichlet problem for Hermitian-Poisson metric equation√(-1)Λ_(ω)G_(H)=λId and proves the existence of Hermitian-Poisson metrics on flat bundles over a class of complete Hermitian manifolds.Whenλ=0,the HermitianPoisson metric is a Hermitian harmonic metric.