Publication details
Pseudo-Riemannian manifolds with recurrent spinor fields
| Authors | |
|---|---|
| Year of publication | 2013 |
| Type | Article in Periodical |
| Magazine / Source | SIBERIAN MATHEMATICAL JOURNAL |
| Citation | |
| Doi | http://dx.doi.org/10.1134/S0037446613040034 |
| Keywords | pseudo-Riemannian manifold; recurrent spinor field; holonomy algebra |
| Description | 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. |