Thickenings and conformal gravity

A twistor correspondence is given for complex conformal space-times with vanishing Bach and Eastwood-Dighton tensors; when the Weyl curvature is algebraically general, these equations are precisely the conformal version of Einstein's vacuum equations with cosmological constant. This gives a fully curved version of the linearized correspondence of Baston and Mason B-M].Research supported in part by NSF grant DMS-8704401