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arXiv · 1002.2064

Pseudo-Riemannian manifolds with recurrent spinor fields

Anton S. Galaev
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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.

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Anton S. Galaev. 2010-02-10. Pseudo-Riemannian manifolds with recurrent spinor fields. https://doi.org/10.1134/s0037446613040034

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