Characterizations of Complex Finsler Metrics

被引:2
作者
Li, Hongjun [1 ]
Xia, Hongchuan [2 ]
机构
[1] Henan Univ, Sch Math & Stat, Kaifeng 475004, Peoples R China
[2] Xinyang Normal Univ, Sch Math & Stat, Xinyang 464000, Peoples R China
基金
中国国家自然科学基金;
关键词
Chern-Finsler connection; Canonical connection; Holomorphic sectional curvature tensor; Balanced complex Finsler metric; Rund Kahler-Finsler-like metric; CONNECTIONS;
D O I
10.1007/s12220-023-01272-3
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Munteanu (Complex spaces in Finsler, Lagrange and Hamilton Geometries, Kluwer Academic Publishers, Dordrecht, 2004) defined the canonical connection associated to a strongly pseudoconvex complex Finsler manifold (M, F). We first prove that the holomorphic sectional curvature tensors of the canonical connection coincide with those of the Chern-Finsler connection associated to F if and only if F is a Kahler-Finsler metric. We also investigate the relationship of the Ricci curvatures (resp. scalar curvatures) of these two connections when M is compact. As an application, two characterizations of balanced complex Finsler metrics are given. Next, we obtain a sufficient and necessary condition for a balanced complex Finsler metric to be Kahler-Finsler. Finally, we investigate conformal transformations of a balanced complex Finsler metric.
引用
收藏
页数:27
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