Compact Kähler manifolds with nonpositive bisectional curvature

Gang Liu*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

Let (Mn, 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 Nk with c1 <  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.

Original languageEnglish (US)
Pages (from-to)1591-1607
Number of pages17
JournalGeometric and Functional Analysis
Volume24
Issue number5
DOIs
StatePublished - Sep 1 2014

ASJC Scopus subject areas

  • Analysis
  • Geometry and Topology

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