Holomorphic sectional curvature of complex Finsler manifolds

TL;DR

This paper establishes inequalities involving holomorphic sectional curvature in complex Finsler manifolds, deriving a Schwarz Lemma and exploring conditions for negative Kodaira dimension.

Contribution

It introduces new curvature inequalities and applies them to derive a Schwarz Lemma and conditions for negative Kodaira dimension in complex Finsler geometry.

Findings

Derived a curvature inequality for complex Finsler metrics.

Proved a Schwarz Lemma for maps from Riemannian to Finsler manifolds.

Identified conditions under which complex Finsler manifolds have negative Kodaira dimension.

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.