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A Toponogov-Type Comparison Theorem for Finsler Manifolds and its Applications

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Abstract

In this paper, we introduce the notion of modified flag curvature for Finsler metrics which naturally come from Hessian comparison theorem. We then establish a Toponogov-type comparison theorem for Finsler manifolds with nonnegative-modified flag curvature. As its applications, we prove that the fundamental group of any forward complete Finsler manifold (M, F) with nonnegative-modified flag curvature is finitely generated; furthermore, if additional M has bounded Cartan tensor, then M is of finite topological type.

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Authors and Affiliations

  1. Department of Mathematics, Minjiang University, Fuzhou, 350121, Fujian, P. R. China

    Bing-Ye Wu

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  1. Bing-Ye Wu
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Correspondence to Bing-Ye Wu.

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Communicated by Jost-Hinrich Eschenburg.

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Wu, BY. A Toponogov-Type Comparison Theorem for Finsler Manifolds and its Applications. Bull. Iran. Math. Soc. 45, 1531–1543 (2019). https://doi.org/10.1007/s41980-019-00213-7

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  • DOI: https://doi.org/10.1007/s41980-019-00213-7

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