A Liouville property of holomorphic maps

TL;DR

This paper proves a Liouville property for holomorphic maps between specific complete Kahler manifolds, under curvature conditions, extending understanding of their rigidity and behavior.

Contribution

It establishes a new Liouville theorem for holomorphic maps under curvature assumptions, broadening previous results in complex differential geometry.

Findings

Holomorphic maps are constant under given curvature conditions

Extension of Liouville theorems to broader classes of Kahler manifolds

Provides conditions ensuring rigidity of holomorphic maps

Abstract

In this article, we prove a Liouville property of holomorphic maps from a complete Kahler manifold with nonnegative holomorphic bisectional curvature to a complete simply connected Kahler manifold with a certain assumption on the sectional curvature.