Parallel spinors on Lorentzian Weyl spaces
arXiv:2007.07615 · doi:10.1007/s00605-021-01569-x
Abstract
Holonomy algebras of Lorentzian Weyl spin manifolds with weighted parallel spinors are found. For Lorentzian Weyl manifolds admitting recurrent null vector fields are introduced special local coordinates similar to Kundt and Walker ones. Using that, the local form of all Lorentzian Weyl spin manifolds with weighted parallel spinors is given. The Einstein-Weyl equation for the obtained Weyl structures is analyzed and examples of Einstein-Weyl spaces with weighted parallel spinors are given.
arXiv commentThe final version to appear in Monatshefte für Mathematik
References in corpus (13)
- Einstein-Weyl geometry, the dKP equation and twistor theory
- Breaking the M-waves
- Pseudo-Riemannian metrics with parallel spinor fields and vanishing Ricci tensor
- On the Einstein-Weyl and conformal self-duality equations
- On the local structure of Lorentzian Einstein manifolds with parallel distribution of null lines
- Einstein--Weyl Spaces and Near-Horizon Geometry
- Geometric structures of vectorial type
- Parallel spinors and holonomy groups on pseudo-Riemannian spinmanifolds
- Spin structures on compact homogeneous pseudo-Riemannian manifolds
- Holonomy groups of Lorentzian manifolds
- Spinor equations in Weyl geometry
- On supersymmetric Einstein-Weyl spaces
- How to find the holonomy algebra of a Lorentzian manifold