2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/137893We study the intrinsic geometry of hypersurfaces in Calabi-Yau manifolds of real dimension 6 and, more generally, SU(2)-structures on 5-manifolds defined by a generalized Killing spinor. We prove that in the real analytic case, such a 5-manifold can be isometrically embedded as a hypersurface in a Calabi-Yau manifold in a natural way. We classify nilmanifolds carrying invariant structures of this type, and present examples of the associated metrics with holonomy SU(3).30 pages. v2: corrected the statement and proof of Theorem 14; added a comment on the embedding property in the non-real-analytic caseDifferential Geometry53C25 (Primary) 14J32, 53C29, 53C42, 58A15 (Secondary)text