Actions of semisimple Lie groups preserving a degenerate Riemannian metric

TL;DR

This paper proves a rigidity result for the lightcone in Minkowski space, showing it is uniquely characterized by its degenerate Riemannian metric and the presence of a semi-simple group action.

Contribution

It establishes the uniqueness of the lightcone as the only space with a lightlike degenerate metric supporting a non-proper semi-simple group action.

Findings

The lightcone's structure is rigid under semi-simple group actions.

It is essentially the unique space with a degenerate lightlike metric supporting such symmetries.

Abstract

We prove a rigidity of the lightcone in Minkowski space. It is essentially the unique space endowed with a degenerate Riemannian metric, of lightlike type, and supporting an isometric non-proper action of a semi-simple group.