3-dimensional left-invariant sub-Lorentzian contact structures

TL;DR

This paper classifies 3-dimensional contact Lie groups with specific sub-Lorentzian structures using invariants derived from a normal Cartan connection, advancing understanding of geometric structures in Lorentzian settings.

Contribution

It introduces a classification framework for 3D contact Lie groups with sub-Lorentzian structures based on Cartan invariants, a novel approach in the field.

Findings

Complete classification of $ts$-invariant sub-Lorentzian structures on 3D contact Lie groups.

Identification of key invariants from the normal Cartan connection.

Framework applicable to further geometric and control theory studies.

Abstract

We provide a classification of $ts$-invariant sub-Lorentzian structures on $3$ dimensional contact Lie groups. Our approach is based on invariants arising form the construction of a normal Cartan connection.