  The main result of this paper is that a Lorentzian manifold is locally
conformally equivalent to a manifold with recurrent lightlike vector field and
totally isotropic Ricci tensor if and only if its conformal tractor holonomy
admits a 2-dimensional totally isotropic invariant subspace. Furthermore, for
semi-Riemannian manifolds of arbitrary signature we prove that the conformal
holonomy algebra of a $C$-space is a Berger algebra. For Ricci-flat spaces we
show how the conformal holonomy can be obtained by the holonomy of the ambient
metric and get results for Riemannian manifolds and plane waves.
