ACTION OF SEMISIMPLE ISOMERY GROUPS ON SOME RIEMANNIAN MANIFOLDS OF NONPOSITIVE CURVATURE
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Abstract:
A manifold with a smooth action of a Lie group G is called G-manifold. In this paper we consider a complete Riemannian manifold M with the action of a closed and connected Lie subgroup G of the isometries. The dimension of the orbit space is called the cohomogeneity of the action. Manifolds having actions of cohomogeneity zero are called homogeneous. A classic theorem about Riemannian manifolds of nonpositive curvature states that a homogeneous Riemannian manifold of nonpositive curvature is diffeomorphic to ...
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Journal title
volume 3 issue 11
pages 51- 58
publication date 2017-10-23
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