On Ricci flat metrics possessing non-trivial conformal Killing algebras

We prove that a non-trivial conformal Killing algebra with bidimensional orbits of a 4-dimensional pseudo-Riemannian manifold is isomorphic to the Rotondaro algebra either of dimension 3, or of 4.We also give an exact description of Ricci flat 4-metrics that admit a non-trivial conformal Killing algebra with bidimensional orbits.