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Geodesic orbit spheres and constant curvature in Finsler geometry. (English) Zbl 1404.53094

The author generalizes the classification of geodesic orbit metrics on spheres from [Yu. G. Nikonorov, Vladikavkaz. Mat. Zh. 15, No. 3, 67–76 (2013; Zbl 1293.53062)] to Finsler geometry. Also it is proved that a homogeneous Finsler sphere of constant flag curvature \(K=1\) is a geodesic orbit space iff it is Randers.

MSC:

53C60 Global differential geometry of Finsler spaces and generalizations (areal metrics)
22E46 Semisimple Lie groups and their representations
53C22 Geodesics in global differential geometry

Citations:

Zbl 1293.53062
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References:

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