The Penrose transform and complex integral geometry

A survey is given of results on the representation of solutions of systems of massless equations in terms of solutions of the Cauchy–Riemann equations on the space of Penrose twisters. A detailed introduction to the theory of twistors is given. The basic integral transform — the Penrose transformation — is investigated by means of complex integral geometry. Other approaches to the theory of twistors are discussed and compared. In addition, the Yang–Mills equation is considered from the point of view of nonlinear Cauchy–Riemann equations.