Conformally homogeneous Lorentzian spaces

In this paper, we prove that if a one-connected non-conformally flat conformal Lorentzian manifold [Formula: see text] admits a connected essential transitive group of conformal transformations, then there exists a metric [Formula: see text] such that [Formula: see text] is a complete homogeneous plane wave. This completes the classification of one-connected Lorentzian manifolds that admit a transitive essential conformal group. We also prove that the group of conformal transformations of a non-conformally flat one-connected homogeneous plane wave [Formula: see text] consists of homotheties, and it is a one-dimensional extension of the group of isometries.