Lorentzian similarity manifold

TL;DR

This paper studies Lorentzian similarity manifolds, which are conformally flat Lorentzian manifolds modeled on a specific group, exploring their properties through developing maps and holonomy representations.

Contribution

It characterizes compact Lorentzian similarity manifolds and analyzes their properties using geometric tools like developing maps and holonomy.

Findings

Contains Lorentzian flat space forms

Properties of compact Lorentzian similarity manifolds analyzed

Uses developing maps and holonomy representations

Abstract

If an $m+2$-manifold $M$ is locally modeled on $\RR^{m+2}$ with coordinate changes lying in the subgroup $G=\RR^{m+2}\rtimes ({\rO}(m+1,1)\times \RR^+)$ of the affine group ${\rA}(m+2)$, then $M$ is said to be a \emph{Lorentzian similarity manifold}. A Lorentzian similarity manifold is also a conformally flat Lorentzian manifold because $G$ is isomorphic to the stabilizer of the Lorentz group ${\rPO}(m+2,2)$ which is the full Lorentzian group of the Lorentz model $S^{2n+1,1}$. It contains a class of Lorentzian flat space forms. We shall discuss the properties of compact Lorentzian similarity manifolds using developing maps and holonomy representations.