English

Holomorphic sectional curvature of complex Finsler manifolds

Differential Geometry 2019-08-21 v2

Abstract

In this paper, we get an inequality in terms of holomorphic sectional curvature of complex Finsler metrics. As applications, we prove a Schwarz Lemma from a complete Riemannian manifold to a complex Finsler manifold. We also show that a strongly pseudoconvex complex Finsler manifold with semi-positive but not identically zero holomorphic sectional curvature has negative Kodaira dimension under an extra condition.

Keywords

Cite

@article{arxiv.1710.10246,
  title  = {Holomorphic sectional curvature of complex Finsler manifolds},
  author = {Xueyuan Wan},
  journal= {arXiv preprint arXiv:1710.10246},
  year   = {2019}
}

Comments

20 pages, revised version, to appear in The Journal of Geometric Analysis