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The Flag Curvature Tensor on a Closed Finsler Space

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Abstract

In this article, we characterize two particular closed Finsler spaces in terms of the flag curvature tensor. That is, with respect to the \({\cal L}_{2}\)inner product of the space of all symmetric 2-tensor on the projective sphere bundle, a Finsler structure has Landsberg (Berwald resp.) type if and only if its flag curvature tensor is orthogonal to some given line (plane resp.). Using a result of Akbar-Zadeh we give a unifying description for three special closed Finsler manifolds.

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Authors and Affiliations

  1. School of Mathematical Sciences, Peking University, Beijing, 100871, P. R. China

    Xiaohuan Mo

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  1. Xiaohuan Mo
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Correspondence to Xiaohuan Mo.

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The author was supported by Wang KC Foundation of Hong Kong and the National Natural Science Foundation of China

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Mo, X. The Flag Curvature Tensor on a Closed Finsler Space. Results. Math. 36, 149–159 (1999). https://doi.org/10.1007/BF03322108

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  • DOI: https://doi.org/10.1007/BF03322108

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