2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/78944Let V be the pseudo-Euclidean vector space of signature (p,q), p>2 and W a module over the even Clifford algebra Cl^0 (V). A homogeneous quaternionic manifold (M,Q) is constructed for any spin(V)-equivariant linear map Π: \wedge^2 W \to V. If the skew symmetric vector valued bilinear form Πis nondegenerate then (M,Q) is endowed with a canonical pseudo-Riemannian metric g such that (M,Q,g) is a homogeneous quaternionic pseudo-Kähler manifold. The construction is shown to have a natural mirror in the category of supermanifolds. In fact, for any spin(V)-equivariant linear map Π: Sym^2 W \to V a homogeneous quaternionic supermanifold (M,Q) is constructed and, moreover, a homogeneous quaternionic pseudo-Kähler supermanifold (M,Q,g) if the symmetric vector valued bilinear form Πis nondegenerate.to appear in the Memoirs of the AMS, 81 pages, Latex source fileDifferential Geometry53C25; 53C30text