Conformally flat Lorentzian manifolds with special holonomy groups

TL;DR

This paper classifies conformally flat Lorentzian manifolds with special holonomy, identifying their local metrics as extensions of constant curvature Riemannian spaces to Walker metrics.

Contribution

It provides the first local classification of such manifolds, linking conformal flatness, special holonomy, and Walker metrics.

Findings

Classification of conformally flat Lorentzian manifolds with special holonomy

Identification of local metrics as extensions of constant curvature spaces

Connection between conformal flatness and Walker metrics

Abstract

The local classification of conformally flat Lorentzian manifolds with special holonomy groups is obtained. The corresponding local metrics are certain extensions of Riemannian spaces of constant sectional curvature to Walker metrics.