Cohomogeneity one actions on Minkowski spaces

TL;DR

This paper classifies and analyzes isometric cohomogeneity one actions on Minkowski spaces, revealing complex orbit structures including non-Hausdorff orbit spaces and orbit-equivalence phenomena on degenerate subspaces.

Contribution

It provides a classification of cohomogeneity one actions on low-dimensional Minkowski spaces and explores orbit space properties and orbit-equivalence complexities.

Findings

Existence of non-Hausdorff orbit spaces.

Orbit-equivalence varies on degenerate subspaces.

Complete classification in 2- and 3-dimensional cases.

Abstract

We study isometric cohomogeneity one actions on the (n+1)-dimensional Minkowski space up to orbit-equivalence. We give examples of isometric cohomogeneity one actions on the Minkowski space whose orbit spaces are non-Hausdorff. We show that there exist isometric cohomogeneity one actions on the Minkowski space which are orbit-equivalent on the complement of an n-dimensional degenerate subspace and not orbit-equivalent on this degenerate subspace. We classify isometric cohomogeneity one actions on 2- and 3-dimensional Minkowski spaces up to orbit-equivalence.