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1. CJM 2009 (vol 62 pp. 52)

Deng, Shaoqiang
 An Algebraic Approach to Weakly Symmetric Finsler Spaces In this paper, we introduce a new algebraic notion, weakly symmetric Lie algebras, to give an algebraic description of an interesting class of homogeneous Riemann--Finsler spaces, weakly symmetric Finsler spaces. Using this new definition, we are able to give a classification of weakly symmetric Finsler spaces with dimensions $2$ and $3$. Finally, we show that all the non-Riemannian reversible weakly symmetric Finsler spaces we find are non-Berwaldian and with vanishing S-curvature. This means that reversible non-Berwaldian Finsler spaces with vanishing S-curvature may exist at large. Hence the generalized volume comparison theorems due to Z. Shen are valid for a rather large class of Finsler spaces. Keywords:weakly symmetric Finsler spaces, weakly symmetric Lie algebras, Berwald spaces, S-curvatureCategories:53C60, 58B20, 22E46, 22E60
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