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• W3099835285 abstract "In this paper, we establish a sufficient condition for a geodesic in a Riemannian manifold to be homogeneous, i.e. an orbit of an $1$-parameter isometry group. As an application of this result, we provide a new proof of the fact that every weakly symmetric space is geodesic orbit manifold, i.e. all its geodesics are homogeneous. We also study general properties of homogeneous geodesics, in particular, the structure of the closure of a given homogeneous geodesic. We present several examples where this closure is a torus of dimension $geq 2$ which is (respectively, is not) totally geodesic in the ambient manifold. Finally, we discuss homogeneous geodesics in Lie groups supplied with left-invariant Riemannian metrics." @default.
• W3099835285 created "2020-11-23" @default.
• W3099835285 creator A5047975487 @default.
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• W3099835285 date "2018-12-01" @default.
• W3099835285 modified "2023-10-06" @default.
• W3099835285 title "On homogeneous geodesics and weakly symmetric spaces" @default.
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• W3099835285 doi "https://doi.org/10.1007/s10455-018-9641-1" @default.
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