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arXiv · 2511.03713

A local Lorentzian Ferrand-Obata theorem for conformal vector fields

Sorin Dumitrescu·Charles Frances·Karin Melnick·Vincent Pecastaing·Abdelghani Zeghib
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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.

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Sorin Dumitrescu, Charles Frances, Karin Melnick, Vincent Pecastaing, Abdelghani Zeghib. 2025-11-05. A local Lorentzian Ferrand-Obata theorem for conformal vector fields. https://arxiv.org/abs/2511.03713

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