Geodesic
An Algebraic Approach to Weakly Symmetric Finsler Spaces
Canadian journal of mathematics, Tome 62 (2010) no. 1, pp. 52-73

Voir la notice de l'article provenant de la source Cambridge University Press

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 $\text{S}$ -curvature. This means that reversible non-Berwaldian Finsler spaces with vanishing $\text{S}$ -curvature may exist at large. Hence the generalized volume comparison theorems due to $\text{Z}$ . Shen are valid for a rather large class of Finsler spaces.
DOI : 10.4153/CJM-2010-004-x
Mots-clés : weakly symmetric Finsler spaces, weakly symmetric Lie algebras, Berwald spaces, S-curvature 
Deng, Shaoqiang. An Algebraic Approach to Weakly Symmetric Finsler Spaces. Canadian journal of mathematics, Tome 62 (2010) no. 1, pp. 52-73. doi: 10.4153/CJM-2010-004-x
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