ACTION OF SEMISIMPLE ISOMERY GROUPS ON SOME RIEMANNIAN MANIFOLDS OF NONPOSITIVE CURVATURE

Subject Areas : Statistics

M. bakhtiari ¹ , R. Mirzaei ²

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.

Received: 2017-04-05 Accepted : 2017-06-05 Published : 2017-10-23

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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