Perfect fluid space-times with a two-dimensional orthogonally transitive group of homothetic motions

We use the GHP formalism to obtain perfect fluid space-times with a two-dimensional and orthogonally transitive group of proper homothetic motions H-2, with the additional condition that the four-velocity of the fluid either lies on the group orbits or is orthogonal to them. In the first case the orbits of the H-2 are timelike and all possible solutions are explicitly given. They comprise (i) space-times of Petrov type I that admit a group H-3 containing two hypersurface orthogonal and commuting Killing vectors (when the H-2 is abelian, the fluid has a stiff equation of state and the space-time is of type D), and (ii) a class of type D static space-times with a maximal H-2 in which the two-spaces orthogonal to the group orbits have constant curvature. When the orbits of the H-2 are spacelike, the fluid is necessarily stiff and different classes of solutions admitting maximal H-2 and H-3 are identified.