Compact Kähler Manifolds with Nonpositive Bisectional Curvature

Abstract

In this article, we prove that for any compact Kähler manifold Mn with real analytic metric and nonpositive bisectional curvature, there exists a finite cover M′ of M such that M′ is a holomorphic and metric fiber bundle over a compact Kähler manifold N with nonpositive bisectional curvature and c1(N) < 0, and the fiber is a flat complex torus. This partially confirms a conjecture of Yau.