A Classification Of Cohomogeneity One Actions On The Minkowski Space $\mathbb{R}^{3,1}$

TL;DR

This paper classifies cohomogeneity one isometric actions on 4D Minkowski space, detailing group representations and orbit structures for both proper and non-proper cases, advancing understanding of symmetry actions in Lorentzian geometry.

Contribution

It provides a comprehensive classification of cohomogeneity one actions on Minkowski space, including explicit group representations and orbit space descriptions.

Findings

Classification of proper and non-proper actions

Explicit group representations in $O(3,1)\ltimes \mathbb{R}^{3,1}$

Determination of orbits and orbit spaces for proper actions

Abstract

The aim of this paper is to classify cohomogeneity one isometric actions on the 4-dimensional Minkowski space $\mathbb{R}^{3,1}$, up to orbit equivalence. Representations, up to conjugacy, of the acting groups in $O(3,1)\ltimes \mathbb{R}^{3,1}$ are given in both cases, proper and non-proper actions. When the action is proper, the orbits and the orbit spaces are determined.