2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/173171We prove the following to results: (1) A subgroup G of the isometry group of a Riemannian manifold M acts properly on M if and only if G is closed in the isometry group of M. (2) The orbits of an isometric action are closed if and only if the action is orbit equivalent to a proper isometric action.2 pagesDifferential Geometry57S20; 53C30text