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arxiv: 1005.3740 · v1 · submitted 2010-05-20 · 🧮 math.DG

On the three-dimensional homogeneous SO(2) - isotropic Riemannian manifolds

classification 🧮 math.DG
keywords surfacesgeodesicshomogeneousisotropicmanifoldsriemannianthree-dimensionaltotally
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In this paper 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.

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