Compact Hermitian manifolds with quasi-negative curvature. (arXiv:1810.07325v1 [math.DG])

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 a corollary, we show that the canonical line bundle of a compact Hermitian manifold with nonpositive bisectional curvature and quasi-negative Chern-Ricci curvature is ample. 查看全文>>