A uniformization theorem in complex Finsler geometry
Differential Geometry
2021-03-01 v1
Abstract
In complex Finsler geometry, an open problem is: does there exist a weakly K\"ahler Finsler metric which is not K\"ahler? In this paper, we give an affirmative answer to this open problem. More precisely, we construct a family of the weakly K\"ahler Finsler metrics which are non-K\"ahler. The examples belong to the unitary invariant complex Randers metrics. Furthermore, a uniformization theorem of the unitary invariant complex Randers metrics with constant holomorphic curvature is proved under the weakly K\"ahler condition.
Cite
@article{arxiv.2102.13484,
title = {A uniformization theorem in complex Finsler geometry},
author = {Ningwei Cui and Jinhua Guo and Linfeng Zhou},
journal= {arXiv preprint arXiv:2102.13484},
year = {2021}
}