Lorentzian manifolds with transitive conformal group

2016/11/10 by Dmitri V. Alekseevsky, Alekseevsky, Dmitri V.
Mathematics · Medicine · Physics and Astronomy · #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Ophthalmology and Eye Disorders

paper · pdf · doi:10.48550/arxiv.1611.03447

openalex publication_date 2016/11/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study pseudo-Riemanniasn manifolds (M,g) with transitive group of conformal transformation which is essential, i.e. does not preserves any metric conformal to g. All such manifolds of Lorentz signature with non exact isotropy representation of the stability subalgebra are described. A construction of essential conformally homogeneous manifolds with exact isotropy represenatation is given. Using spinor formalism, we prove that it provides all 4-dimensional non conformally flat Lorentzian 4-dimensional manifolds with transitive essentially conformal group.

Related

• Conformally homogeneous Lorentzian spaces
• Three-dimensional conformally symmetric manifolds
• The Lorentzian Lichnerowicz Conjecture for real-analytic, three-dimensional manifolds
• Semi-simple Lie groups acting conformally on compact Lorentz manifolds
• Conformal actions of solvable Lie groups on closed Lorentzian manifolds