On the classification of weakly symmetric Finsler spaces |
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Authors: | Shaoqiang Deng |
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Institution: | 1.School of Mathematical Sciences and LPMC Nankai University,Tianjin,P. R. China |
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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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Keywords: | |
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