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.