2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/76458We prove the existence of a geometric characteristic submanifold for non-positively curved manifolds of any dimension greater than or equal to three. In dimension three, our result is a geometric version of the topological characteristic submanifold theorem due to Jaco, Shalen and Johannson.14 pagesGeometric Topologytext