Radial conformal motions are considered in conformally flat space-times and
their properties are used to obtain conformal factors. The geodesic case l
eads directly to the conformal factor of Robertson-Walker universes. Genera
l cases admitting homogeneous expansion or orthogonal hypersurfaces of cons
tant curvature are analyzed separately. When the two conditions above are c
onsidered together a subfamily of the Stephani perfect fluid solutions, wit
h acceleration Fermi-Walker propagated along the flow of the fluid, follows
. The corresponding conformal factors are calculated and contrasted with th
ose associated with Robertson-Walker space-times. (C) 2000 American Institu
te of Physics. [S0022-2488(00)03007-3].