Compact Kähler Manifolds with Nonpositive Bisectional Curvature

Hung-Hsi Wu; Fangyang Zheng

doi:10.4310/jdg/1090351386

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Compact Kähler Manifolds with Nonpositive Bisectional Curvature

Hung-Hsi Wu Fangyang Zheng

Year: 2002 Journal: Journal of Differential Geometry Vol: 61 (2) Publisher: Lehigh University

DOI: 10.4310/jdg/1090351386

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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.

Keywords:

Mathematics Curvature Metric (unit) Holomorphic function Pure mathematics Manifold (fluid mechanics) Sectional curvature Conjecture Kähler manifold Mathematical analysis Fiber Topology (electrical circuits) Combinatorics Geometry Scalar curvature Materials science Composite material

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Geometry and complex manifolds

Physical Sciences → Mathematics → Geometry and Topology

Geometric Analysis and Curvature Flows

Physical Sciences → Mathematics → Applied Mathematics

Algebraic Geometry and Number Theory

Physical Sciences → Mathematics → Geometry and Topology

Compact Kähler Manifolds with Nonpositive Bisectional Curvature

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