The Cauchy Problems for Einstein Metrics and Parallel Spinors

Zusammenfassung

The restriction of a parallel spinor on some spin manifold to a hypersurface is a generalized Killing spinor on M. We show, conversely, that in the real analytic category, every spin manifold (M, g) carrying a generalized Killing spinor psi can be isometrically embedded as a hypersurface in a spin manifold carrying a parallel spinor whose restriction to M is psi. We also answer negatively the corresponding question in the smooth category.