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On conformal complex Finsler metrics |
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| Authors: | Li Hongjun Qiu Chunhui Xia Hongchuan Zhong Guozhu |
| Institution: | 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 ; |
| Abstract: | In this paper, we study conformal transformations in complex Finsler geometry. We first prove that two weakly Kähler 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 Kähler Finsler. Finally, we discuss conformal transformations of a strongly pseudoconvex complex Finsler metric, which preserve the geodesics, holomorphic S curvatures and mean Landsberg tensors. |
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