The Lorentzian Lichnerowicz Conjecture for real-analytic, three-dimensional manifolds

2021/08/16 by Charles Frances, Frances, Charles, Karin Melnick +1 · 3 citations
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2108.07215

openalex publication_date 2021/08/16 · openalex created_date 2023/09/06 · openalex updated_date 2026/07/28

Abstract

Given a compact, three-dimensional, real-analytic Lorentzian manifold (M,g), we prove that the identity component of the conformal group preserves a metric in the conformal class [g], or (M,g) is conformally flat.

Cited by

• Pseudo-Conformal actions of semisimple Lie groups
• A local Lorentzian Ferrand-Obata theorem for conformal vector fields
• Failure of Lichnerowicz-type result in parabolic geometries of real rank at least 3

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