In this work, we show that along a particular choice of Hermitian curvature flow, the non-positivity of the first Ricci curvature will be preserved if the initial metric has Griffiths non-positive Chern curvature. If in addition, the first Ricci curvature is negative at a point, then the canonical line bundle is ample.

中文翻译：

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具有准负曲率的厄米流形

在这项工作中，我们表明，沿着厄米曲率流的特定选择，如果初始度量具有格里菲斯非正陈曲率，则第一个 Ricci 曲率的非正性将被保留。此外，如果第一个 Ricci 曲率在一点处为负，则规范线丛是充足的。