Hermitian manifolds with quasi-negative curvature

Abstract

In this work, we show that along a particular choice of Hermitian curvature flow, the non-positivity of Chern-Ricci curvature will be preserved if the initial metric has non-positive bisectional curvature. As an application, we show that the canonical line bundle of a compact Hermitian manifold with nonpositive bisectional curvature and quasi-negative Chern-Ricci curvature is ample.

final version to appear in Math. Ann. arXiv admin note: text overlap with arXiv:1812.04610

References in corpus (2)

• Negative Holomorphic curvature and positive canonical bundle
• An extension of a theorem of Wu-Yau