Ricci solitons of special Lorentzian Lie groups with a four-dimensional isometry group

TL;DR

This paper classifies specific four-dimensional Lorentzian Lie groups with isometry groups, showing they are all non-gradient expanding Ricci solitons, and provides explicit global coordinate descriptions.

Contribution

It identifies and describes a unique class of homogeneous Lorentzian three-manifolds with four-dimensional isometry groups, proving they are non-gradient expanding Ricci solitons.

Findings

All such manifolds are non-gradient expanding Ricci solitons.

Explicit global coordinate descriptions of these manifolds are provided.

The class studied is distinct from Lorentzian Bianchi-Cartan-Vranceanu spaces and plane waves.

Abstract

In the framework of the study of homogeneous Lorentzian three-manifolds, we consider here the only class of examples which admit a four-dimensional group of isometries but are neither Lorentzian Bianchi-Cartan-Vranceanu spaces nor plane waves. We obtain an explicit description in global coordinates of these special homogeneous Lorentzian manifolds. We then prove that all such examples are non-gradient expanding Ricci solitons.