Abstract
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.
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Podestà, F., Spiro, A. Some topological properties of cohomogeneity one manifolds with negative curvature. Ann Glob Anal Geom 14, 69–79 (1996). https://doi.org/10.1007/BF00128196
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DOI: https://doi.org/10.1007/BF00128196