Hermitian manifolds with semi-positive holomorphic sectional curvature

Xiaokui Yang

Hermitian manifolds with semi-positive holomorphic sectional curvature

Differential Geometry 2016-04-14 v4 Complex Variables

Authors: Xiaokui Yang

Abstract

We prove that a compact Hermitian manifold with semi-positive but not identically zero holomorphic sectional curvature has Kodaira dimension $-\infty$ . 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.

Keywords

hermitian manifold holomorphic sectional curvature kodaira dimension kodaira surface hyperelliptic surface nef tangent bundle

Cite

@article{arxiv.1412.5252,
  title  = {Hermitian manifolds with semi-positive holomorphic sectional curvature},
  author = {Xiaokui Yang},
  journal= {arXiv preprint arXiv:1412.5252},
  year   = {2016}
}

Comments

We condense the paper according to the referee's suggestions

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