Curvatures of strongly convex Kähler-Finsler manifolds
Curvatures of strongly convex Kähler-Finsler manifolds
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DOI：
10.1016/j.difgeo.2022.101957
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发表时间：
2023-02
影响因子：
0.5
通讯作者：
Hongjun Li;Chunhui Qiu;Guozhu Zhong
中科院分区：
文献类型：
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作者：
Hongjun Li;Chunhui Qiu;Guozhu Zhong
在这篇文章中，我们研究了强凸（弱）Kähler-Finsler流形上的曲率。首先，我们证明了强凸弱Kähler-Finsler流形上的全纯平面截面的全纯截面曲率只是旗曲率的一半。其次，我们比较了强凸Kähler-Finsler流形上Rund联络与Chern-Finsler联络或复Berward联络的曲率。最后讨论了旗曲率与全纯双截曲率之间的关系，并比较了强凸Kähler-Finsler流形上的两种S-曲率.
In this article, we study curvatures on a strongly convex (weakly) Kähler-Finsler manifold. First, we prove that the holomorphic sectional curvature is just half of the flag curvature in a holomorphic plane section on a strongly convex weakly Kähler-Finsler manifold. Second, we compare curvatures associated to the Rund connection with curvatures associated to the Chern-Finsler connection or the complex Berward connection on a strongly convex Kähler-Finsler manifold. Finally, we discuss relationships between flag curvatures and holomorphic bisectional curvatures, and compare two kinds ofS-curvatures on a strongly convex Kähler-Finsler manifold.