A local Lorentzian Ferrand-Obata theorem for conformal vector fields
Differential Geometry
2025-11-06 v1 Dynamical Systems
Abstract
For a conformal vector field on a closed, real-analytic, Lorentzian manifold we prove that the flow is locally isometric -- that it preserves a metric in the conformal class on a neighborhood of any point -- or the metric is everywhere conformally flat. The main theorem can be viewed as a local version of the Lorentzian Lichnerowicz conjecture in the real-analytic setting. The key result is an optimal improvement of the local normal forms for conformal vector fields of [FM13], which focused on non-linearizable singularities. This article is primarily concerned with essential linearizable singularities, and the proofs include global arguments which rely on the compactness assumption.
Cite
@article{arxiv.2511.03713,
title = {A local Lorentzian Ferrand-Obata theorem for conformal vector fields},
author = {Sorin Dumitrescu and Charles Frances and Karin Melnick and Vincent Pecastaing and Abdelghani Zeghib},
journal= {arXiv preprint arXiv:2511.03713},
year = {2025}
}