A uniformization theorem in complex Finsler geometry

Ningwei Cui; Jinhua Guo; Linfeng Zhou

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arXiv · 2102.13484

A uniformization theorem in complex Finsler geometry

Ningwei Cui·Jinhua Guo·Linfeng Zhou

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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.

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Ningwei Cui, Jinhua Guo, Linfeng Zhou. 2021-02-26. A uniformization theorem in complex Finsler geometry. https://arxiv.org/abs/2102.13484

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