The conformal group of a compact simply connected Lorentzian manifold

TL;DR

This paper proves that the conformal group of a closed, simply connected, real analytic Lorentzian manifold is compact, extending previous results on isometry groups and supporting the Lorentzian Lichnerowicz Conjecture.

Contribution

It establishes the compactness of the conformal group for such manifolds, providing a significant advancement in Lorentzian geometry and conformal group classification.

Findings

Conformal group of the manifold is compact.

Supports the Lorentzian Lichnerowicz Conjecture.

Extends D'Ambra's results to conformal groups.

Abstract

We prove that the conformal group of a closed, simply connected, real analytic Lorentzian manifold is compact. D'Ambra proved in 1988 that the isometry group of such a manifold is compact. Our result implies the Lorentzian Lichnerowicz Conjecture for real analytic Lorentzian manifolds with finite fundamental group. Third version includes corrections and clarifications, particularly in section 6.