2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/61644We prove that, from an Einstein manifold of dimension greater than or equal to five, there are just two types of harmonic morphism with one-dimensional fibres. This generalizes a result of R.L. Bryant who obtained the same conclusion under the assumption that the domain has constant curvature.Latex 2e, 21 pagesDifferential Geometry58E20 (Primary) 53C43 (Secondary)text