Pseudo-Riemannian manifolds with recurrent spinor fields

Details Pseudo-Riemannian manifolds with recurrent spinor fields Pseudo-Riemannian manifolds with recurrent spinor fields

2010-02-10

arxiv.org/abs/1002.2064v1

Mathematics

Differential Geometry

12 pages

Scientific paper

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 classify holonomy algebras of simply connected Riemannian and Lorentzian manifolds and irreducible holonomy algebras of pseudo-Riemannian manifolds, whose spinor bundles admit such subbundles.

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