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Journal of Differential Geometry 61 (2002), 263-287.

Compact Kähler manifolds with nonpositive bisectional curvature

Hung-Hsi Wu & Fangyang Zheng

Abstract:

In this article, we prove that for any compact K\"{a}hler manifold $M^n$ 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 K\"{a}hler manifold $N$ with nonpositive bisectional curvature and $c_1(N)<0$, and the fiber is a flat complex torus. This partially confirms a conjecture of Yau.