Perfect fluid spheres admitting a one-parameter group of conformal motions

Some exact analytical solutions of the Einstein equations for perfect fluids were found under the assumption of spherical symmetry and the existence of a one-parameter group of conformal motions. The first solution exhibited represents a nonstatic homogeneous spherically symmetric distribution of matter which is singular at t=0. Two other solutions represent contracting and expanding fluids, respectively, whose evolution tends asymptotically to a static sphere with a surface gravitational potential equal to (1)/(3) . These two solutions possess vanishing pressure surfaces which are not the boundary of matter except in the static limit. Finally an oscillating distribution of matter is presented.