Homogeneous Lorentz manifolds with simple isometry group

TL;DR

This paper classifies certain Lorentzian homogeneous spaces with simple isometry groups, showing how subgroups relate to standard Lorentz groups in specific cases.

Contribution

It provides a classification of invariant Lorentz metrics on homogeneous spaces for specific simple Lie groups, identifying conjugacy classes of subgroups.

Findings

For G=SO(2,n), the subgroup H is conjugate to SO(1,n).

For G=SO(1,n), the subgroup H is conjugate to SO(1,n-1).

The results specify the structure of Lorentz homogeneous manifolds with simple isometry groups.

Abstract

Let H be a closed, noncompact subgroup of a simple Lie group G, such that G/H admits an invariant Lorentz metric. We show that if G = SO(2,n), with n > 2, then the identity component of H is conjugate to the identity component of SO(1,n). Also, if G = SO(1,n), with n > 2, then the identity component of H is conjugate to the identity component of SO(1,n-1).