K\"ahler Finsler manifolds with curvatures bounded from below

Bin Chen; Nan Li; Siwei Liu

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arXiv · 2207.00703

K\"ahler Finsler manifolds with curvatures bounded from below

Bin Chen·Nan Li·Siwei Liu

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Abstract

We obtain a partial parallelism of the complex structure on K\"ahler Finsler manifolds. As applications, we prove Synge-Tsukamoto theorem and Bonnet-Myers theorem for positively curved K\"ahler Finsler manifolds. Moreover, we generalize a comparison theorem due to Ni-Zheng by introducing the notion of orthogonal Ricci curvature to K\"ahler Finsler geometry.

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Bin Chen, Nan Li, Siwei Liu. 2022-07-02. K\"ahler Finsler manifolds with curvatures bounded from below. https://arxiv.org/abs/2207.00703

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