Parallel spinors on Lorentzian Weyl spaces
Differential Geometry
2022-10-10 v3 Mathematical Physics
math.MP
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.
Cite
@article{arxiv.2007.07615,
title = {Parallel spinors on Lorentzian Weyl spaces},
author = {Andrei Dikarev and Anton S. Galaev},
journal= {arXiv preprint arXiv:2007.07615},
year = {2022}
}
Comments
The final version to appear in Monatshefte f\"ur Mathematik