Characterizations of Complex Finsler Metrics
Characterizations of Complex Finsler Metrics
复制标题
DOI：
10.1007/s12220-023-01272-3
复制
发表时间：
2021-10
期刊：
影响因子：
--
通讯作者：
Hongjun Li;Hongchuan Xia
中科院分区：
文献类型：
--
作者：
Hongjun Li;Hongchuan Xia
Munteanu（Complex spaces in Finsler，拉格朗日and汉密尔顿Geometries，Kluwer Academic Publishers，多尔德雷赫特，2004）定义了与强伪凸复Finsler流形（M，F）相关联的正则联络。我们首先证明了正则联络的全纯截面曲率张量与对应于F的Chern-Finsler联络的全纯截面曲率张量重合，当且仅当F是Kähler-Finsler度量.我们还研究了Ricci曲率（分别）的关系。标量曲率）的这两个连接时，M是紧凑的。作为应用，给出了平衡复Finsler度量的两个刻画.其次，我们得到了平衡复Finsler度量是Kähler-Finsler度量的一个充要条件。最后，我们研究了平衡复Finsler度量的共形变换。
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 toFif and only ifFis a Kähler-Finsler metric. We also investigate the relationship of the Ricci curvatures (resp. scalar curvatures) of these two connections whenMis 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 Kähler-Finsler. Finally, we investigate conformal transformations of a balanced complex Finsler metric.