An Algebraic Approach to Weakly Symmetric Finsler Spaces
Canadian journal of mathematics, Tome 62 (2010) no. 1, pp. 52-73
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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.
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
@article{10_4153_CJM_2010_004_x,
author = {Deng, Shaoqiang},
title = {An {Algebraic} {Approach} to {Weakly} {Symmetric} {Finsler} {Spaces}},
journal = {Canadian journal of mathematics},
pages = {52--73},
year = {2010},
volume = {62},
number = {1},
doi = {10.4153/CJM-2010-004-x},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2010-004-x/}
}
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