Fabio Podesta, Andrea Spiro
Compact Quotients of Negatively Curved Riemannian Manifolds with Large Isometry Group
Preprint series: ESI preprints

MSC:

53C30 Homogeneous manifolds, See also {14M15, 14M17, 32M10,

57S25 Groups acting on specific manifolds

Abstract: A definition of locally cohomogeneity
one Riemannian manifold is given and it is proved that a compact,
negatively curved Riemannian manifold of local cohomogeneity one is
locally symmetric; this result extends a well known theorem, due to
Heintze, stating the local symmetry of a negatively curved, compact,
locally homogeneous Riemannian manifold. As a corollary, we get that a
non symmetric chomogeneity one Riemannian manifold admits no
compact quotients.

Keywords: Cohomogeneity one, G-manifolds, negative curvatur