Symmetries of Lorentzian Three-Manifolds with Recurrent Curvature

TL;DR

This paper classifies the symmetries of Lorentzian three-manifolds with recurrent curvature, focusing on those with special geometric structures like Walker manifolds, and extends some results to a broader class.

Contribution

It provides a complete classification of symmetries related to curvature for Lorentzian three-manifolds with recurrent curvature, including Ricci, matter, and Weyl collineations.

Findings

Full classification of symmetries for these manifolds

Identification of symmetries related to curvature

Extension of results to broader Walker manifolds

Abstract

Locally homogeneous Lorentzian three-manifolds with recurrect curvature are special examples of Walker manifolds, that is, they admit a parallel null vector field. We obtain a full classification of the symmetries of these spaces, with particular regard to symmetries related to their curvature: Ricci and matter collineations, curvature and Weyl collineations. Several results are given for the broader class of three-dimensional Walker manifolds.