2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/69202We consider the unique Hermitian connection with totally skew-symmetric torsion on a Hermitian manifold. We prove that if the torsion is parallel and the holonomy is Sp(n)U(1), considered as a subgroup of U(2n) x U(1), then the manifold is locally isomorphic to the twistor space of a quaternionic Kaehler manifold with positive scalar curvature. If the manifold is complete, then it is globally isomorphic to such a twistor space.24 pages; some inessential changesDifferential Geometry53B05; 53B35; 53C26; 53C55text