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VOL. 3 | 2002 Topological Properties of Some Cohomogeneity One Riemannian Manifolds of Nonpositive Curvature
R. Mirzaie, S. Kashani

Editor(s) Ivaïlo M. Mladenov, Gregory L. Naber


In this paper we study some non-positively curved Riemannian manifolds acted on by a Lie group of isometries with principal orbits of codimension one. Among other results it is proved that if the universal covering manifold satisfies some conditions then every non-exceptional singular orbit is a totally geodesic submanifold. When $M$ is flat and is not toruslike, it is proved that either each orbit is isometric to $\mathbb{R}^k \times \mathbb{T}^m$ or there is a singular orbit. If the singular orbit is unique and non-exceptional, then it is isometric to $\mathbb{R}^k \times \mathbb{T}^m$.


Published: 1 January 2002
First available in Project Euclid: 12 June 2015

zbMATH: 1017.53038
MathSciNet: MR1884859

Digital Object Identifier: 10.7546/giq-3-2002-351-359

Rights: Copyright © 2002 Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences


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