Conformally homogeneous Lorentzian spaces

We prove that if a simply connected non-conformally flat conformal Lorentzian manifold $(M,c)$ admits an essential transitive group of conformal transformations, then there exists a metric $g\in c$ such that $(M,g)$ is a complete homogeneous plane wave. We also prove that the group of conformal tran...

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Bibliographic Details
Main Authors Alekseevsky, Dmitri V, Galaev, Anton S
Format Journal Article
LanguageEnglish
Published 03.07.2024
Subjects
Mathematics - Differential Geometry
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Summary:We prove that if a simply connected non-conformally flat conformal Lorentzian manifold $(M,c)$ admits an essential transitive group of conformal transformations, then there exists a metric $g\in c$ such that $(M,g)$ is a complete homogeneous plane wave. We also prove that the group of conformal transformations of a non-conformally flat simply connected homogeneous plane wave $(M,g)$ consists of homotheties, hence it is a 1-dimensional extension of the group of isometries.
DOI:10.48550/arxiv.2407.03095