Hermitian manifolds with semi-positive holomorphic sectional curvature

2014/12/17 by Xiaokui Yang, Yang, Xiaokui · 1 citation
Mathematics · #32J25 #32L15 #53C55 #Algebraic Geometry and Number Theory #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1412.5252

openalex publication_date 2014/12/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that a compact Hermitian manifold with semi-positive but not identically zero holomorphic sectional curvature has Kodaira dimension -∞. As applications, we show that Kodaira surfaces and hyperelliptic surfaces can not admit Hermitian metrics with semi-positive holomorphic sectional curvature although they have nef tangent bundles.

Citations

• A theorem on holonomy
• Complex parallisable manifolds
• On the canonical line bundle and negative holomorphic sectional curvature
• Scalar curvature and uniruledness on projective manifolds
• Big vector bundles and compact complex manifolds with semi-positive tangent bundles
• Optimal pinching for the holomorphic sectional curvature of Hitchin's metrics on Hirzebruch surfaces

Cited by

• Hermitian manifolds with nonpositive holomorphic sectional curvature

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