Work

Classification of closed conformally flat Lorentzian manifolds with unipotent holonomy

Year: 2026

Type: article

Abstract: We classify closed, conformally flat Lorentzian manifolds of dimension with unipotent holonomy in PO(2,n). They are all Kleinian and fall into four different geometric types according to the intersection of the image of the developing map with a holonomy‐invariant isotropic flag. They are homeomorphic to or to a nilmanifold of degree at most three, up to a finite cover. We classify those admitting an essential conformal flow; these fall into two geometric types, both homeomorphic to up to finite cover.

Source: Journal of Topology

DOI: 10.1112/topo.70085

Authors: Rachel Lee, Karin Melnick

Institutions: University of Maryland, College Park, University of Luxembourg

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: National Science Foundation

Awards: Dynamics and the Classification of Geometries on Manifolds, Transformation Groups in Conformal and Projective Geometry