Complex Manifolds With Negative Curvature Operator

2019/11/14 by Man-Chun Lee, Jeffrey Streets · 1 citation
Mathematics · #Geometry and complex manifolds #Geometric Analysis and Curvature Flows #Algebraic Geometry and Number Theory #Mathematics #Curvature #Operator (biology) #Mathematical proof #Convergence (economics) #Pure mathematics #Canonical bundle #Negative curvature #Flow (mathematics) #Mathematical analysis #Geometry

paper · doi:10.1093/imrn/rnz331

openalex publication_date 2019/11/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Abstract We prove that compact complex manifolds admitting metrics with negative Chern curvature operator either admit a d d^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.

Citations

• Three-manifolds with positive Ricci curvature
• The uniformization theorem for compact Kähler manifolds of nonnegative holomorphic bisectional curvature
• Four-manifolds with positive curvature operator
• La 1-forme de torsion d'une vari�t� hermitienne compacte
• Manifolds with positive curvature operators are space forms
• Manifolds with 1/4-pinched curvature are space forms
• On real bisectional curvature for Hermitian manifolds

Cited by

• Kähler manifold [wikipedia]

Related

• Complex manifolds with negative curvature operator
• Hermitian metrics on complex non-Kähler manifolds
• Complex product manifolds cannot be negatively curved
• Chern-Ricci flows on noncompact complex manifolds
• Manifolds with positive curvature operators are space forms