  We consider spin manifolds with an Einstein metric, either Riemannian or
indefinite, for which there exists a Killing spinor. We describe the intrinsic
geometry of nondegenerate hypersurfaces in terms of a PDE satisfied by a pair
of induced spinors, akin to the generalized Killing spinor equation.
Conversely, we prove an embedding result for real analytic pseudo-Riemannian
manifolds carrying a pair of spinors satisfying this condition.
