Work

Conformally homogeneous Lorentzian spaces

Year: 2025

Type: article

Abstract: In this paper, we prove that if a one-connected non-conformally flat conformal Lorentzian manifold [Formula: see text] admits a connected essential transitive group of conformal transformations, then there exists a metric [Formula: see text] such that [Formula: see text] is a complete homogeneous plane wave. This completes the classification of one-connected Lorentzian manifolds that admit a transitive essential conformal group. We also prove that the group of conformal transformations of a non-conformally flat one-connected homogeneous plane wave [Formula: see text] consists of homotheties, and it is a one-dimensional extension of the group of isometries.

Source: Communications in Contemporary Mathematics

DOI: 10.1142/s0219199725500828

Authors: Dmitri V. Alekseevsky, Anton S. Galaev

Institutions: Moscow Institute of Physics and Technology, University of Hradec Králové

Language: English

Topic: Advanced Differential Geometry Research

Subfield: Astronomy and Astrophysics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: green

Funder: Grantová Agentura České Republiky

Award: Graded differential geometry with applications