2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/33388We study cohomogeneity one Riemannian manifolds and we establish some simple criterium to test when a singular orbit is totally geodesic. As an application, we classify compact, positively curved Riemannian manifolds which are acted on isometrically by a non semisimple Lie group with an hypersurface orbit.13 pagesDifferential Geometry53C21 57S15 (Primary)text