Affine Hermitian-Einstein metrics (Q1024912)

The present paper is a very useful study of affine Hermitian-Einstein metrics on holomorphic vector bundles. The main result is Theorem 1: Let \(M\) be a compact special affine manifold without boundary equipped with an affine Gauduchon metric \(g\). Let \(E\rightarrow M\) be a flat complex vector bundle. If \(E\) is \(g\)-stable then there is an affine Hermitian-Einstein metric on \(E\).