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On homogeneous Finsler spaces. (English) Zbl 1137.53339

Summary: We study homogeneous Finsler spaces and show that they are forward complete. As a special case we consider homogeneous Randers spaces and show that if these spaces have constant flag curvature then the underlying Riemannian space is locally symmetric. Also we extend some of classical results in Riemannian homogeneous spaces to homogeneous Finsler spaces.

MSC:

53C60 Global differential geometry of Finsler spaces and generalizations (areal metrics)
53C35 Differential geometry of symmetric spaces
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