ACTION OF SEMISIMPLE ISOMERY GROUPS ON SOME RIEMANNIAN MANIFOLDS OF NONPOSITIVE CURVATURE
Subject Areas : Statistics
1 - Department of Mathematics, Faculty of Science, Imam Khomeini International University (IKIU), Qazvin, Iran.
2 - Department of Mathematics, Faculty of Science, Imam Khomeini International University (IKIU), Qazvin, Iran.
Keywords: خمینههای حاصلضربی, گروه لی نیم ساده, G-خمینه, نقص همگنی,
Abstract :
A manifold with a smooth action of a Lie group Gis called G-manifold. In this paper we consider a complete Riemannian manifold Mwith the action of a closed and connected Lie subgroup Gof 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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