On conformal supergravity and projective superspace

The projective superspace formulation for four-dimensional = 2 matter-coupled supergravity presented in arXiv:0805.4683 makes use of the variant superspace realization for the = 2 Weyl multiplet in which the structure group is SL(2,) × SU(2) and the super-Weyl transformations are generated by a covariantly chiral parameter. An extension to Howe's realization of = 2 conformal supergravity in which the tangent space group is SL(2,) × U(2) and the super-Weyl transformations are generated by a real unconstrained parameter was briefly sketched. Here we give the explicit details of the extension.