  We study the stationary and axisymmetric non-convective differentially
rotating perfect-fluid solutions of Einstein's field equations admitting one
conformal symmetry. We analyse the two inequivalent Lie algebras not
exhaustively considered in Mars and Senovilla, 1994, and show that the general
solution for each Lie algebra depends on one arbitrary function of one of the
coordinates while a set of three ordinary differential equations for four
unknowns remains to be solved. The conformal Killing vector of these solutions
is necessarily homothetic. We summarize in a table all the possible solutions
for all the allowed Lie algebras and also add a corrigendum to an erroneous
statement in the paper quated above concerning the differentially rotating
character of one of the solutions presented
