Structure of asymptotic twistor space

We show that asymptotic projective twistor space PT+ is an Einstein--Kaehler manifold of positive curvature. We then use the Chern--Moser theory of hypersurfaces in complex manifolds to show that the Kaehler curvature of PT+ closely related to the CR curvature of its boundary. We also give a proof that the Kaehler potential function defining the boundary satisfies the complex Monge--Ampere equations