Pseudo-Riemannian manifolds with recurrent spinor fields

Abstract

The existence of a recurrent spinor field on a pseudo-Riemannian spin manifold $(M,g)$ is closely related to the existence of a parallel 1-dimensional complex subbundle of the spinor bundle of $(M,g)$. We characterize the following simply connected pseudo-Riemannian manifolds admitting such subbundles in terms of their holonomy algebras: Riemannian manifolds; Lorentzian manifolds; pseudo-Riemannian manifolds with irreducible holonomy algebras; pseudo-Riemannian manifolds of neutral signature admitting two complementary parallel isotropic distributions.

13 pages, the final version

References in corpus (3)

• Metrics that realize all Lorentzian holonomy algebras
• Parallal Spinors on Pseudo-Riemannian SpinC Manifolds
• Ricci-Flat Holonomy: a Classification

Cited by in corpus (3)

• Pure spinors, intrinsic torsion and curvature in even dimensions
• Pure spinors, intrinsic torsion and curvature in odd dimensions
• Parallel spinors for ${\mathrm{G}}_2^{\ast }$ and isotropic structures