Chern-Ricci curvatures, holomorphic sectional curvature and Hermitian metrics

• 作者: Haojie Chen Lingling Chen Xiaolan Nie
• 来源期刊: 中国科学：数学（英文版）
• 年，卷（期）: 2021,（4）
• 所属期刊栏目: Articles
• 页码范围: 763-780
• 页数: 18页
• 语种: 英文

摘要

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