English

K\"ahler Finsler manifolds with curvatures bounded from below

Differential Geometry 2022-12-27 v2

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.

Keywords

Cite

@article{arxiv.2207.00703,
  title  = {K\"ahler Finsler manifolds with curvatures bounded from below},
  author = {Bin Chen and Nan Li and Siwei Liu},
  journal= {arXiv preprint arXiv:2207.00703},
  year   = {2022}
}