  Among all plastic deformations of the gravitational Lorentz vacuum \cite{wr1}
a particular role is being played by conformal deformations. These are
conveniently described by using the homogeneous space for the conformal group
SU(2,2)/S(U(2)x U(2)) and its Shilov boundary - the compactified Minkowski
space \tilde{M} [1]. In this paper we review the geometrical structure involved
in such a description. In particular we demonstrate that coherent states on the
homogeneous Kae}hler domain give rise to Einstein-like plastic conformal
deformations when extended to \tilde{M} [2].
