2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/107617We study transversely Lorentzian foliations on the closed 3-manifolds. We classify them under a completeness hypothesis and we deduce the dual classification of codimension 1 geodesically complete timelike totally geodesic foliations. Besides we provide an example of a Lorentzian foliation on a compact 3-manifold which is equicontinuous on a proper dense open subset of the manifold, and hence not transversely complete.27 pages, 3 figuresDifferential GeometryDynamical Systems53C12 (primary) ; 53C50 (secondary)text