2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/61670We prove that all generalised symmetric spaces of compact simple Lie groups are formal in the sense of Sullivan. Nevertheless, many of them, including all the non-symmetric flag manifolds, do not admit Riemannian metrics for which all products of harmonic forms are harmonic.18 pages; minor corrections; to appear in Mathematical Proceedings of the Cambridge Philosophical SocietyDifferential GeometryAlgebraic Topology57T15 (Primary) 53C35, 55P62, 58A14 (Secondary)text