Classification of Closed Conformally Flat Lorentzian 3-Manifolds with Unipotent Holonomy

Abstract

A conformally flat manifold is a manifold that is locally conformally equivalent to a flat affine space. In this thesis, we classify closed conformally flat Lorentzian manifolds of dimension three whose holonomy group is unipotent. More specifically, we show that such a manifold is finitely covered by either $S^2\times S^1$ or a parabolic torus bundle. Furthermore, we show that such a manifold is Kleinian and is essential if and only if it can be covered by $S^2\times S^1$.