Space-times admitting a three-parameter similarity group
  Spacetimes admitting a similarity group are considered. Amongst them, special attention is given to the 3-parameter ones. A classification of such spacetimes is given based on the Bianchi type of the similarity group $H_3$, and the general form of the metric is provided in each case assuming the orbits are non-null. 
J. Carot, L. Mas, A.M. Sintes