Invariant conformal vectors in space-times admitting a group of G3 of motions acting on spacelike orbits S2

The paper deals with four-dimensional space-times admitting locally a three-dimensional group of motions G3 acting on two-dimensional spacelike orbits S2. The local existence problem for conformal vectors invariant under G3 is shown to be equivalent to the local existence problem for Killing vectors of a given two-dimensional pseudo-Riemannian metric g. This problem is explicitly solved in terms of the Gaussian curvature R of g and two of its scalar differential concomitants. The results are applied to the case of dust-filled space-times, where an exhaustive list of metrics has been obtained by using the algebraic computing language Smp. The metrics are either homogeneous, self-similar, or Friedmann models