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arXiv · 1905.02950

Chern-Ricci curvatures, holomorphic sectional curvature and Hermitian metrics

Haojie Chen·Lingling Chen·Xiaolan Nie
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Abstract

We present some formulae related to the Chern-Ricci curvatures and scalar curvatures of special Hermitian metrics. We prove that a compact locally conformal Kähler manifold with constant nonpositive holomorphic sectional curvature is Kähler. We also give examples of complete non-Kähler metrics with pointwise negative constant but not globally constant holomorphic sectional curvature, and complete non-Kähler metric with zero holomorphic sectional curvature and nonvanishing curvature tensor.

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Haojie Chen, Lingling Chen, Xiaolan Nie. 2019-05-08. Chern-Ricci curvatures, holomorphic sectional curvature and Hermitian metrics. https://arxiv.org/abs/1905.02950

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