Proceedings of the International Conference on Geometry, Integrability and Quantization

Topological Properties of Some Cohomogeneity One Riemannian Manifolds of Nonpositive Curvature

R. Mirzaie and S. Kashani

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

Article information

Source
Proceedings of the Third International Conference on Geometry, Integrability and Quantization, Ivaïlo M. Mladenov and Gregory L. Naber, eds. (Sofia: Coral Press Scientific Publishing, 2002), 351-359

Dates
First available in Project Euclid: 12 June 2015

Permanent link to this document
https://projecteuclid.org/ euclid.pgiq/1434145481

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

Mathematical Reviews number (MathSciNet)
MR1884859

Zentralblatt MATH identifier
1017.53038

Citation

Mirzaie, R.; Kashani, S. Topological Properties of Some Cohomogeneity One Riemannian Manifolds of Nonpositive Curvature. Proceedings of the Third International Conference on Geometry, Integrability and Quantization, 351--359, Coral Press Scientific Publishing, Sofia, Bulgaria, 2002. doi:10.7546/giq-3-2002-351-359. https://projecteuclid.org/euclid.pgiq/1434145481


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