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COHOMOGENEITY ONE RIEMANNIAN MANIFOLDS OF CONSTANT POSITIVE CURVATURE
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 Title & Authors
COHOMOGENEITY ONE RIEMANNIAN MANIFOLDS OF CONSTANT POSITIVE CURVATURE
Abedi, Hosein; Kashani, Seyed Mohammad Bagher;
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 Abstract
In this paper we study non-simply connected Riemannian manifolds of constant positive curvature which have an orbit of codimension one under the action of a connected closed Lie subgroup of isometries. When the action is reducible we characterize the orbits explicitly. We also prove that in some cases the manifold is homogeneous.
 Keywords
cohomogeneity one;constant positive curvature;
 Language
English
 Cited by
 References
1.
A. V. Alekseevsky and D. V. Alekseevsky, G-manifolds with one-dimensional orbit space, Lie groups, their discrete subgroups, and invariant theory, 1-31, Adv. Soviet Math. 8, Amer. Math. Soc., Providence, RI, 1992

2.
A. V. Alekseevsky and D. V. Alekseevsky, Riemannian G-manifold with one-dimensional orbit space, Ann. Global Anal. Geom. 11 (1993), no. 3, 197-211

3.
H. Borel, Some remarks about Lie groups transitive on spheres and tori, Bull. Amer. Math. Soc. 55 (1949). 580-587 crossref(new window)

4.
J. Dadok, Polar coordinates induced by actions of compact Lie groups, Trans. Amer. Math. Soc. 288 (1985), no. 1, 125-137 crossref(new window)

5.
A. Kollross, A classification of hyperpolar and cohomogeneity one actions, Trans. Amer. Math. Soc. 354 (2002), no. 2, 571-612 crossref(new window)

6.
F. Podestµa and L. Verdiani, Positively curved 7-dimensional manifolds, Quart. J. Math. Oxford Ser. (2) 50 (1999), no. 200, 497-504 crossref(new window)

7.
C. Searle, Cohomogeneity and positive curvature in low dimensions, Math. Z. 214 (1993), no. 3, 491-498 crossref(new window)

8.
E. Straume, Compact connected Lie transformation groups on spheres with low cohomogeneity. I., Mem. Amer. Math. Soc. 119 (1996), no. 569

9.
J. A. Wolf, Spaces of constant curvature, McGraw-Hill Book Co., New York-London-Sydney 1967