Killing spinors and hypersurfaces

Abstract

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.

22 pages, correction to the exponent of the imaginary unit in equation (12), sign correction in equation 14, other minor corrections

References in corpus (3)

• New G2 holonomy cones and exotic nearly Kaehler structures on the 6-sphere and the product of a pair of 3-spheres
• The Cauchy problem for parallel spinors as first-order symmetric hyperbolic system
• Solvable Lie algebras are not that hypo

Cited by in corpus (1)

• Parallel spinors for ${\mathrm{G}}_2^{\ast }$ and isotropic structures