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Paper Information

Journal:   JOURNAL OF NEW RESEARCHES IN MATHEMATICS   FALL 2017 , Volume 3 , Number 11 ; Page(s) 51 To 58.
 
Paper: 

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

 
 
Author(s):  MIRZAEI R., BAKHTIARI M.*
 
* DEPARTMENT OF MATHEMATICS, FACULTY OF SCIENCE, IMAM KHOMEINI INTERNATIONAL UNIVERSITY (IKIU), QAZVIN, IRAN
 
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…

 
Keyword(s): PRODUCT MANIFOLDS, SEMISIMPLE LIE GROUP, G-MANIFOLD, COHOMOGENEITY
 
 
References: 
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Citations: 
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+ Click to Cite.
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. https://www.sid.ir/en/journal/ViewPaper.aspx?id=569723



Vancouver: Copy

MIRZAEI R., BAKHTIARI M.. ACTION OF SEMISIMPLE ISOMERY GROUPS ON SOME RIEMANNIAN MANIFOLDS OF NONPOSITIVE CURVATURE. JOURNAL OF NEW RESEARCHES IN MATHEMATICS. 2017 [cited 2021July27];3(11 ):51-58. Available from: https://www.sid.ir/en/journal/ViewPaper.aspx?id=569723



IEEE: Copy

MIRZAEI, R., BAKHTIARI, M., 2017. ACTION OF SEMISIMPLE ISOMERY GROUPS ON SOME RIEMANNIAN MANIFOLDS OF NONPOSITIVE CURVATURE. JOURNAL OF NEW RESEARCHES IN MATHEMATICS, [online] 3(11 ), pp.51-58. Available: https://www.sid.ir/en/journal/ViewPaper.aspx?id=569723.



 
 
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