Classification of third-order symmetric Lorentzian manifolds

TL;DR

This paper classifies third-order symmetric Lorentzian manifolds, revealing they are characterized by a special class of pp-waves that extend Cahen-Wallach spaces and second-order symmetric Lorentzian spaces.

Contribution

It provides a complete classification of third-order symmetric Lorentzian manifolds, identifying their structure as a specific type of pp-waves.

Findings

Third-order symmetric Lorentzian manifolds are classified.

They are characterized by a special class of pp-waves.

These manifolds generalize Cahen-Wallach spaces and second-order symmetric spaces.

Abstract

Third-order symmetric Lorentzian manifolds, i.e. Lorentzian manifold with zero third derivative of the curvature tensor, are classified. These manifolds are exhausted by a special type of pp-waves, they generalize Cahen-Wallach spaces and second-order symmetric Lorentzian spaces.