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.
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。
