Lorentzian manifolds with transitive conformal group

We study pseudo-Riemanniasn manifolds (M; g) with transitive group of conformal transformation which is essential, i.e. does not preserves any metric conformal to g. All such manifolds of Lorentz signature with non exact isotropy representation of the stability subalgebra are described. A construction of essential conformally homogeneous manifolds with exact isotropy represenatation is given. Using spinor formalism, we prove that it provides all 4-dimensional non conformally at Lorentzian 4-dimensional manifolds with transitive essentially conformal group.