On conformal complex Finsler metrics  

作　　者：Hongjun Li Chunhui Qiu Hongchuan Xia Guozhu Zhong 

机构地区：[1]School of Mathematics and Statistics,Henan University,Kaifeng 475004,China [2]School of Mathematical Sciences,Xiamen University,Xiamen 361005,China [3]School of Mathematics and Statistics,Xinyang Normal University,Xinyang 464000,China

出　　处：《Science China Mathematics》2022年第7期1517-1530,共14页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant Nos.12001165,11971401,12071386,11701494 and 11971415);Postdoctoral Research Foundation of China(Grant No.2019M652513);Postdoctoral Research Grant in Henan Province(Grant No.19030050);the Nanhu Scholars Program for Young Scholars of Xinyang Normal University。

摘　　要：In this paper,we study conformal transformations in complex Finsler geometry.We first prove that two weakly Kahler Finsler metrics cannot be conformal.Moreover,we give a necessary and sufficient condition for a strongly pseudoconvex complex Finsler metric to be locally conformal weakly Kahler Finsler.Finally,we discuss conformal transformations of a strongly pseudoconvex complex Finsler metric,which preserve the geodesics,holomorphic S-curvatures and mean Landsberg tensors.

关 键 词：weakly Kahler Finsler metric locally conformal weakly Kahler Finsler metric GEODESIC holomorphic S-curvature mean Landsberg tensor 

分 类 号：O186[理学—数学]