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

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MIRZAEI R.; BAKHTIARI M.

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Journal: JOURNAL OF NEW RESEARCHES IN MATHEMATICS Year:2017 | Volume:3 | Issue:11 Page(s): 51-58

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Title

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

Author(s)

MIRZAEI R. | BAKHTIARI M. | Issue Writer Certificate

Keywords

PRODUCT MANIFOLDSQ1

SEMISIMPLE LIE GROUPQ1

G-MANIFOLDQ1

COHOMOGENEITYQ1

Abstract

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 M of nonpositive curvature is diffeomorphic to Rk ×Tm, dim M=m+k. There are many interesting theorems about topological properties of COHOMOGENEITY one G-MANIFOLDs of nonpositive curvature. It is proved that if M is a negatively curved COHOMOGENEITY one Riemannian G-MANIFOLD and dim M>3, then either M is diffeomorphic to, Rk ×Tm, dim M=m+k or p1 (M) =Z.Also, we know that if M is a G –manifold of negative curvature and G is semisimple, then M is simply…

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APA: Copy

MIRZAEI, R., & BAKHTIARI, M.. (2017). ACTION OF SEMISIMPLE ISOMERY GROUPS ON SOME RIEMANNIAN MANIFOLDS OF NONPOSITIVE CURVATURE. JOURNAL OF NEW RESEARCHES IN MATHEMATICS, 3(11 ), 51-58. SID. https://sid.ir/paper/257328/en

Vancouver: Copy

MIRZAEI R., BAKHTIARI M.. ACTION OF SEMISIMPLE ISOMERY GROUPS ON SOME RIEMANNIAN MANIFOLDS OF NONPOSITIVE CURVATURE. JOURNAL OF NEW RESEARCHES IN MATHEMATICS[Internet]. 2017;3(11 ):51-58. Available from: https://sid.ir/paper/257328/en

IEEE: Copy

R. MIRZAEI, and M. BAKHTIARI, “ACTION OF SEMISIMPLE ISOMERY GROUPS ON SOME RIEMANNIAN MANIFOLDS OF NONPOSITIVE CURVATURE,” JOURNAL OF NEW RESEARCHES IN MATHEMATICS, vol. 3, no. 11 , pp. 51–58, 2017, [Online]. Available: https://sid.ir/paper/257328/en

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