  We 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).
