Complex manifolds with negative curvature operator

2019/03/29 by Man-Chun Lee, Jeffrey Streets, Lee, Man-Chun +1 · 3 citations
Mathematics · #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #math.CV #math.DG

paper · pdf · doi:10.48550/arxiv.1903.12645

arxiv created 2019/03/29 · arxiv updated 2019/04/01

Abstract

We prove that compact complex manifolds with admitting metrics with negative Chern curvature operator either admit a dd^c-exact positive (1,1) current, or are Kähler with ample canonical bundle. In the case of complex surfaces we obtain a complete classification. The proofs rely on a global existence and convergence result for the pluriclosed flow.

Cited by

• Hermitian manifolds with nonpositive holomorphic sectional curvature
• Deformations of Non-Kähler Hyperbolicity Notions and Modifications of Degenerate Balanced Manifolds
• Constant kth-mixed curvature

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• Hermitian metrics on complex non-Kähler manifolds
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