Holomorphic sectional curvature of complex Finsler manifolds

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.

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

References in corpus (2)

• Negative Holomorphic curvature and positive canonical bundle
• An extension of a theorem of Wu-Yau

Cited by in corpus (2)

• A Schwarz lemma for weakly Kähler-Finsler manifolds
• Curvature formulas related to a family of stable Higgs bundles