Classification of closed conformally flat Lorentzian manifolds with unipotent holonomy

We classify closed, conformally flat Lorentzian manifolds of dimension n 3 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 S^n-1 S¹ or 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 S^n-1 S¹ up to finite cover.