Affine transformations and parallel lightlike vector fields on compact   Lorentzian $3$-manifolds
  We describe the compact Lorentzian $3$-manifolds admitting a parallel lightlike vector field. The classification of compact Lorentzian $3$-manifolds admitting non-isometric affine diffeomorphisms follows, together with the complete description of these morphisms. Such a Lorentzian manifold is in some sense an equivariant deformation of a flat one. 
Charles Boubel (IRMA), Pierre Mounoud (IMB)
math.DG