An Algebraic Approach to Weakly Symmetric Finsler Spaces
2010 ◽
Vol 62
(1)
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pp. 52-73
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Keyword(s):
AbstractIn 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. Thismeans that reversible non-Berwaldian Finsler spaces with vanishing S-curvaturemay exist at large. Hence the generalized volume comparison theorems due to Z. Shen are valid for a rather large class of Finsler spaces.
1993 ◽
Vol 03
(04)
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pp. 447-489
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2011 ◽
Vol 181
(1)
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pp. 29-52
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2003 ◽
Vol 18
(30)
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pp. 5541-5612
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2010 ◽
Vol 60
(4)
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pp. 570-573
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2016 ◽
Vol 110
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pp. 25-29
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1985 ◽
Vol 38
(3)
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pp. 330-350
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2013 ◽
Vol 65
(1)
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pp. 66-81
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