Prescribed Chern scalar curvatures on complete noncompact Hermitian manifolds with nonpositive curvatures

TL;DR

This paper studies the problem of prescribing Chern scalar curvatures on complete noncompact Hermitian manifolds with nonpositive curvatures, providing conditions for the existence of metrics with constant negative Chern scalar curvature.

Contribution

It establishes new sufficient conditions for the existence of constant negative Chern scalar curvature metrics in the conformal class of such manifolds.

Findings

Existence results for prescribed Chern scalar curvatures on noncompact Hermitian manifolds.

Conditions under which a constant negative Chern scalar curvature metric exists.

Advances in understanding curvature problems on noncompact complex manifolds.

Abstract

In this paper, we investigate the problem of prescribing Chern scalar curvatures on complete noncompact Hermitian manifolds with nonpositive curvatures, and establish some existence results. In particular, we obtain some sufficient conditions for the existence of a constant negative Chern scalar curvature metric in the conformal class.