Conformally homogeneous Lorentz manifolds. II (Q2366345)

[For a review of Part I see Zbl 0695.53051.] The author studies a Lorentzian non-conformally flat manifold \(M\) which admits an essential transitive group \(G\) on conformal transformations. He assumes that the isotropy group \(G_p\) of a point \(p\) contains a non-contractive and non-expanding linear transformation, which is represented in a suitable basis by a matrix of the form \(e^\mu\text{diag}(e^\nu, S, e^{-\nu})\), where \(S\) is an orthogonal matrix. The author proves that if \(M\) is not conformally flat, then \(a= {2\mu\over \nu}\in \{0, 1, 2\}\). In the paper under review, he assumes that \(a= 0\) or 2 and proves that the manifold \(M\) is locally conformally diffeomorphic to a manifold with plane wave metric under some additional conditions. Some results about the global structure of such a manifold \(M\) are also established.