2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/76497This paper determines which orientable hyperbolic 3-manifolds contain simple closed geodesics. The Fuchsian group corresponding to the thrice-punctured sphere generates the only example of a complete non-elementary orientable hyperbolic 3-manifold that does not contain a simple closed geodesic. We do not assume that the manifold is geometrically finite or that it has finitely generated fundamental group.7 pages, to appear in the Bulletin of the London Mathematical SocietyGeometric TopologyDifferential Geometry53C22text