Cohomogeneity one actions on anti de Sitter spacetimes

TL;DR

This paper classifies cohomogeneity one group actions on anti de Sitter spacetimes, providing new examples and detailed subgroup orbit structures, advancing understanding of symmetry actions in Lorentzian geometry.

Contribution

It offers a comprehensive classification of cohomogeneity one actions on anti de Sitter spaces and introduces new nonproper examples and subgroup orbit analyses.

Findings

Classification of cohomogeneity one actions on $AdS^{2n+1}$

New examples of nonproper actions on $AdS^{n+1}$

Determination of parabolic Lie subgroup orbits in $AdS^{n+1}$

Abstract

In this paper we classify, up to orbit equivalence, cohomogeneity one actions of connected closed Lie subgroups of $U(1,n)$ on the $(2n+1)$-dimensional anti de Sitter spacetime $AdS^{2n+1}$. We also give some new examples of nonproper cohomogeneity one actions on $AdS^{n+1}$ and determine parabolic Lie subgroups of $SO(2,n)$ and their orbits in $AdS^{n+1}$