An integral transform on a cylinder and the twistor correspondence

Twistor correspondences for RR-invariant indefinite self-dual conformal structures on R4R4 are established explicitly. These correspondences are written down by using a natural integral transform from functions on a two dimensional cylinder to functions on the flat Lorentz space R1,2R1,2 which is related to the wave equation and the Radon transform. A general method on the twistor construction of indefinite self-dual 4-spaces and indefinite Einstein–Weyl 3-spaces are also summarized.