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arXiv · 1112.1479

Compact Kähler manifolds with nonpositive bisectional curvature

Gang Liu
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Abstract

Let $(M^n, g)$ be a compact Kähler manifold with nonpositive bisectional curvature. We show that a finite cover is biholomorphic and isometric to a flat torus bundle over a compact Kähler manifold $N^k$ with $c_1 < 0$. This confirms a conjecture of Yau. As a corollary, for any compact Kähler manifold with nonpositive bisectional curvature, the Kodaira dimension is equal to the maximal rank of the Ricci tensor. We also prove a global splitting result under the assumption of certain immersed complex submanifolds.

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Gang Liu. 2014-04-29. Compact Kähler manifolds with nonpositive bisectional curvature. https://arxiv.org/abs/1112.1479

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