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On the classification of weakly symmetric Finsler spaces

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Abstract

In this paper, we give the classification of some special types of weakly symmetric Finsler spaces. We first present a general principle to classify weakly symmetric Finsler spaces and also give a method to figure out the Berwald spaces among the class of weakly symmetric Finsler spaces. Then we give an explicit classification of weakly symmetric Finsler spaces with reductive isometric groups as well as the left invariant weakly symmetric Finsler metrics on nilpotent Lie groups of the Heisenberg type. As an application, we obtain a large number of high-dimensional examples of reversible Finsler spaces which are non-Berwaldian and with vanishing S-curvature, a kind of spaces which are sought after in an open problem of Z. Shen.

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Authors and Affiliations

  1. School of Mathematical Sciences and LPMC Nankai University, Tianjin, P. R. China

    Shaoqiang Deng

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  1. Shaoqiang Deng
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Correspondence to Shaoqiang Deng.

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Supported by NSFC (No.10671096 and 10971104) of China.

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Deng, S. On the classification of weakly symmetric Finsler spaces. Isr. J. Math. 181, 29–52 (2011). https://doi.org/10.1007/s11856-011-0002-z

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  • DOI: https://doi.org/10.1007/s11856-011-0002-z

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