Compact quotients of Cahen-Wallach spaces

TL;DR

This paper establishes conditions under which Cahen-Wallach spaces, a class of symmetric Lorentzian manifolds, admit compact quotients, linking geometric properties to algebraic parameters.

Contribution

It provides necessary and sufficient criteria for the existence of compact quotients of Cahen-Wallach spaces based on their defining parameters.

Findings

Derived explicit conditions for compact quotients

Connected geometric structures with algebraic parameters

Enhanced understanding of Lorentzian symmetric spaces

Abstract

Indecomposable symmetric Lorentzian manifolds of non-constant curvature are called Cahen-Wallach spaces. Their isometry classes are described by continuous families of real parameters. We derive necessary and sufficient conditions for the existence of compact quotients of Cahen-Wallach spaces in terms of these parameters.