A local Lorentzian Ferrand-Obata theorem for conformal vector fields

Summary · qwen2.5:32b

The study proves that a conformal vector field on a closed, real-analytic Lorentzian manifold either has a locally isometric flow or results in a metric that is everywhere conformally flat, addressing a local version of the Lorentzian Lichnerowicz conjecture. This work improves upon previous normal forms for conformal vector fields by focusing on essential linearizable singularities and utilizing global arguments dependent on compactness assumptions.

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Mathematical paper discussing local Lorentzian Ferrand-Obata theorem for conformal vector fields on a closed, real-analytic, Lorentzian manifold.

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arXiv:2511.03713v2 Announce Type: replace 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.