Manifolds with non-positive second Chern-Ricci curvature

TL;DR

This paper provides criteria to determine when certain compact Hermitian surfaces with non-positive second Chern-Ricci curvature are Kählerian or projective, advancing understanding of their geometric structure.

Contribution

It introduces a new criterion linking non-positive second Chern-Ricci curvature to Kählerian and projective properties of Hermitian surfaces.

Findings

Established a Kählerian criterion for these surfaces

Linked non-positive second Chern-Ricci curvature to projectivity

Enhanced understanding of Hermitian surface geometry

Abstract

In this paper, we establish a K\"ahlerian or projectivity criterion for a class of compact Hermitian surfaces with non-positive second Chern-Ricci curvature.