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Hermitian manifolds with quasi-negative curvature

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Abstract

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.

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Acknowledgements

The author would like to thank Professor Jeffrey Streets for his interest in this work. He would like to thank Xiaokui Yang for pointing out the related results in [3]. Lastly, he would like to thank Yury Ustinovskiy for patiently answering his questions.

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  1. Department of Mathematics, Northwestern University, 2033 Sheridan Road, Evanston, IL, 60208, USA

    Man-Chun Lee

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  1. Man-Chun Lee
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Correspondence to Man-Chun Lee.

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Communicated by Ngaiming Mok.

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Hermitian manifolds with quasi-negative curvature.

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Lee, MC. Hermitian manifolds with quasi-negative curvature. Math. Ann. 380, 733–749 (2021). https://doi.org/10.1007/s00208-020-01997-4

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