Parallel spinors on Lorentzian Weyl spaces

TL;DR

This paper classifies Lorentzian Weyl spin manifolds with weighted parallel spinors, providing explicit local forms, analyzing Einstein-Weyl equations, and presenting concrete examples of such spaces.

Contribution

It introduces a classification of Lorentzian Weyl spin manifolds with weighted parallel spinors and derives their explicit local forms and Einstein-Weyl solutions.

Findings

Holonomy algebras of these manifolds are characterized.

Explicit local coordinate forms are provided.

Examples of Einstein-Weyl spaces with weighted parallel spinors are constructed.

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.