Nonpostively curved Hermitian metric on product manifolds

TL;DR

This paper classifies all Hermitian metrics with nonpositive holomorphic bisectional curvature on complex product manifolds, extending previous results by Zheng to a broader setting.

Contribution

It generalizes Zheng's classification to all Hermitian metrics on complex product manifolds with nonpositive curvature.

Findings

Complete classification of such metrics.

Extension of Zheng's results to a wider class.

Provides a framework for understanding curvature constraints.

Abstract

In this article, we classify all the Hermitian metrics on a complex product manifold with nonpositive holomorphic bisectional curvature. It is a generalization of a result by Zheng.