Generalized Killing spinors on Einstein manifolds

Abstract

We study generalized Killing spinors on compact Einstein manifolds with positive scalar curvature. This problem is related to the existence compact Einstein hypersurfaces in manifolds with parallel spinors, or equivalently, in Riemannian products of flat spaces, Calabi-Yau, hyperkaehler, G_2 and Spin(7) manifolds.

17 pages; new version including the 2-dimensional case and several stylistical improvements

References in corpus (3)

• Half-flat structures on S^3xS^3
• The Cauchy problems for Einstein metrics and parallel spinors
• The energy-momentum tensor as a second fundamental form

Cited by in corpus (9)

• Generalized Killing spinors and Lagrangian graphs
• Some remarks on polar actions
• Generalized Killing spinors on spheres
• Invariant Spinors on Homogeneous Spheres
• On the spin geometry of supergravity and string theory
• Spinors of real type as polyforms and the generalized Killing equation
• Cauchy spinors on $3$-manifolds
• Homogeneous Sasakian and 3-Sasakian Structures from the Spinorial Viewpoint
• Parallel spinors for ${\mathrm{G}}_2^{\ast }$ and isotropic structures