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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

Abstract

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 $\mathbb{R}^k \times \mathbb{T}^m$.

Information

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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