2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/156685Let (M,g) be a 3-dimensional compact connected real analytic Lorentz manifold and suppose that g is locally homogeneous on a non-empty open set in M (the pseudogroup of local isometries of g has an open orbit). Then we prove that g is locally homogeneous on M (the pseudogroup of local isometries is transitive on M).minor changes; to be published in Ergodic Theory and Dynamical SystemsDifferential Geometry53A55 ; 53B30 ; 53C50text