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On weakly symmetric Finsler spaces. (English) Zbl 1186.53087

Summary: We study weakly symmetric Finsler spaces. We first study an existence theorem of weakly symmetric Finsler spaces. Then we study some geometric properties of these spaces and prove that any such space can be written as a coset space of a Lie group with an invariant Finsler metric. Finally we show that each weakly symmetric Finsler space is of Berwald type.

MSC:

53C60 Global differential geometry of Finsler spaces and generalizations (areal metrics)
53C30 Differential geometry of homogeneous manifolds
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