Classification of closed conformally flat Lorentzian manifolds with unipotent holonomy

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.