Cyclic Lorentzian Lie Groups

TL;DR

This paper classifies three- and four-dimensional Lie groups with cyclic Lorentzian metrics, highlighting differences from the Riemannian case and exploring their geometric properties.

Contribution

It provides a complete classification of low-dimensional cyclic Lorentzian Lie groups, revealing key distinctions from Riemannian cyclic metrics.

Findings

Several results from cyclic Riemannian metrics do not extend to Lorentzian case

Complete classification of three- and four-dimensional cyclic Lorentzian metrics

Identification of unique properties of Lorentzian cyclic Lie groups

Abstract

We consider Lie groups equipped with a left-invariant cyclic Lorentzian metric. As in the Riemannian case, in terms of homogeneous structures, such metrics can be considered as different as possible from bi-invariant metrics. We show that several results concerning cyclic Riemannian metrics do not extend to their Lorentzian analogues, and obtain a full classification of three- and four-dimensional cyclic Lorentzian metrics.