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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

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