2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/77311Classification results are given for (i) compact quaternionic Kähler manifolds with a cohomogeneity-one action of a semi-simple group, (ii) certain complete hyperKähler manifolds with a cohomogeneity-two action of a semi-simple group preserving each complex structure, (iii) compact 3-Sasakian manifolds which are cohomogeneity one with respect to a group of 3-Sasakian symmetries. Information is also obtained about non-compact quaternionic Kähler manifolds of cohomogeneity one and the cohomogeneity of adjoint orbits in complex semi-simple Lie algebras.35 pages, LaTeX + AMS macros Extra hypothesis added to cohomogeneity two hyperKähler classification. To appear in Internat. J. MathDifferential Geometry53C25 (Primary) 14L30, 32L25, 57S25 (Secondary)text