Some topological properties of cohomogeneity one manifolds with negative curvature

✍ Scribed by Fabio Podestà; Andrea Spiro

• Publisher: Springer
• Year: 1996
• Tongue: English
• Weight: 608 KB
• Volume: 14
• Category: Article
• ISSN: 0232-704X
• DOI: 10.1007/bf00128196

✦ Synopsis

This paper is aimed at studying negatively curved Riemannian manifolds acted on by a Lie group of isometries with principal orbits of codimension one. The orbit space of such a manifold M is proved to be always homeomorphic to R or R+ and this second case may occur only when either the singular orbit is a geodesic of M or when the space is simply connected. Several corollaries are given.