Affine transformations and parallel lightlike vector fields on compact Lorentzian 3-manifolds

Abstract

We describe the compact Lorentzian 3 3 -manifolds admitting a parallel lightlike vector field. The classification of compact Lorentzian 3 3 -manifolds admitting nonisometric 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.