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ACTION OF SEMISIMPLE ISOMERY GROUPS ON SOME RIEMANNIAN MANIFOLDS OF NONPOSITIVE CURVATURE | ||
| Journal of New Researches in Mathematics | ||
| مقاله 5، دوره 3، شماره 11، آبان 2017، صفحه 51-58 اصل مقاله (314.42 K) | ||
| نوع مقاله: research paper | ||
| نویسندگان | ||
M. bakhtiari  ؛ R. Mirzaei
| ||
| Department of Mathematics, Faculty of Science, Imam Khomeini International University (IKIU), Qazvin, Iran. | ||
| چکیده | ||
| 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 ... | ||
| کلیدواژهها | ||
| product manifolds؛ semisimple Lie group؛ G-manifold؛ cohomogeneity | ||
| مراجع | ||
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[1] A.V. Alekseevsky and D.V. Alekseevsky, G-manifolds with one dimentional orbit space,
Adv. Sov. Math., 8 (1992) 1-31.
[2] A.V Alekseevsky and D.V Alekseevsky, Riemannian G-manifolds with one dimentional
orbit space, Ann. Glob. Anal. and Geom., 11(1993) 197-211.
[3] D.V Alekseevsky, Homogeneous Riemannian manifolds of negative curvature, Math., Sb. 96( nl)(1975) 93-117.
[4] H. Abedi and D.V. Alekseevsky and S.M.B. Kashani, Cohomogeneity one Riemannian
manifolds of nonpositive curvature, Differential Geometry and its Application, 25 (2007) 561-581.
[5] R. Bishop and B. O'Neill, Manifolds of negative curvature, Trans. Am. Math. Soc., 115 (1969) 1-49.
[6] G. E. Bredon, Introduction to Compact Transformation Groups. Acad. Press. New York and London (1972).
[7] E. Heintze, On homogeneous Riemannian manifolds of negative curvature, Math. Ann,
211 (1974) 1-49.
[8] S. Helgason, Diffrential Geometry Lie Group and Symmetric Spaces. Acad. press. New York (1978).
[9] S. Kobayashi, Homogeneous Riemannian manifolds of negative curvature, Tohoku Math. J., 14 (1962) 413-415.
[10] P. W. Michor, Isometric actions of Lie groups and invariants, Lecture course at the
university of Vienna, 1996-97.
[11] R. Mirzaie, On topology of some Riemannian manifolds of negative curvature with a compact Lie group of isometries, Hokkaido Math. J., 44 (2015) 81-89.
[12] R. Mirzaie, On negatively curved G-manifolds of low cohomogeneity, Hokkaido Math. J., 38 (2009) 797-803.
[13] R. Mirzaie, Actions without nontrivial singular orbits on Riemannian manifolds of negative curvature, Acta Math. Hungar., 147(1) (2015) 172-178.
[14] R. Mirzaie, On Riemannian manifolds of constant negative curvature, J. Korean Math.
Soc., 48 (2011) 21-23.
[15] R. Mirzaie and S.M.B. Kashani, On topological properties of some cohomogeneity one manifolds of nonpositive curvature, Bull. Korean Math. Soc., 37 (2000) 578-599.
[16] R. Mirzaie and H. Soroush, Topology of orbits and orbit space of some product G-
manifolds, Manuscripta Math., 149 (2016) 297-302.
[17] B. O'Neill, Semi-Riemannian Geometry with Application to Relativity, Acad. Press.
New York, Berekley (1983).
[18] F. Podesta and A. Spiro, Some topological properties of cohomogeneity one manifolds
with negative curvature, Ann. Global Anal. Geom., 14 (1996) 69-79.
[19] C. Searle, Cohomogeneity and Positive Curvature in Low Dimensions, M. Z., 214 (1993) 491-498.
[20] J. Wolf, Homogenity and bounded isometries in manifold of negative curvature. III. J. Math., 8 (1964) 14-18.
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