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On the three-dimensional homogeneous \(SO(2)\)-isotropic Riemannian manifolds. (English) Zbl 1249.53017

Summary: We consider some properties of the three-dimensional homogeneous \(SO(2)\)-isotropic Riemannian manifolds. In particular, we determine the geodesics, the totally geodesic surfaces, the totally umbilical surfaces and the geodesics of the rotational surfaces.

MSC:

53B21 Methods of local Riemannian geometry
53C22 Geodesics in global differential geometry
53C30 Differential geometry of homogeneous manifolds
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