  Locally homogeneous Lorentzian three-manifolds with recurrect curvature are
special examples of Walker manifolds, that is, they admit a parallel null
vector field. We obtain a full classification of the symmetries of these
spaces, with particular regard to symmetries related to their curvature: Ricci
and matter collineations, curvature and Weyl collineations. Several results are
given for the broader class of three-dimensional Walker manifolds.
