Two-symmetric Lorentzian manifolds

TL;DR

This paper classifies two-symmetric Lorentzian manifolds, revealing they are composed of specific pp-waves with commutative holonomy, expanding understanding of their geometric structure.

Contribution

It introduces a classification of two-symmetric Lorentzian manifolds using holonomy group methods, identifying their composition and properties.

Findings

Manifolds are exhausted by special pp-waves

They possess commutative holonomy like Cahen-Wallach spaces

Classification advances understanding of Lorentzian geometry

Abstract

We classify two-symmetric Lorentzian manifolds using methods of the theory of holonomy groups. These manifolds are exhausted by a special type of pp-waves and, like the symmetric Cahen-Wallach spaces, they have commutative holonomy.