K\"ahler Finsler manifolds with curvatures bounded from below

Bin Chen; Nan Li; Siwei Liu

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K\"ahler Finsler manifolds with curvatures bounded from below

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arxiv 2207.00703 v2 pith:2ODTOLGH submitted 2022-07-02 math.DG

Bin Chen , Nan Li , Siwei Liu This is my paper

classification math.DG

keywords ahlerfinslermanifoldstheoremapplicationsbelowbonnet-myersbounded

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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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