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Pseudo-Riemannian manifolds with recurrent spinor fields

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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 that admit these subbundles in terms of their holonomy algebras: Riemannian manifolds, Lorentzian manifolds, pseudo-Riemannian manifolds with irreducible holonomy algebras, and pseudo-Riemannian manifolds of neutral signature admitting two complementary parallel isotropic distributions.

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  1. University of Hradec Králové, Hradec Králové, Czech Republic

    A. S. Galaev

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  1. A. S. Galaev
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Correspondence to A. S. Galaev.

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Original Russian Text Copyright © 2013 Galaev A.S.

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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 54, No. 4, pp. 762–774, July–August, 2013.

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Galaev, A.S. Pseudo-Riemannian manifolds with recurrent spinor fields. Sib Math J 54, 604–613 (2013). https://doi.org/10.1134/S0037446613040034

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  • DOI: https://doi.org/10.1134/S0037446613040034

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