2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/152156We study a geometrical condition (PHWC) which is weaker than horizontal weak conformality. In particular, we show that harmonic maps satisfying this condition, which will be called {\em pseudoharmonic morphisms}, include harmonic morphisms and can be described as pulling back certain germs to certain other germs. Finally, we construct a canonical f-structure associated to every map satisfying (PHWC) and find conditions on this f-structure to ensure the harmonicity of the map.AMS-LaTex v1.2b, 13 pagesDifferential Geometry58E20 (Primary) 53C15 (Secondary)text