## ABSTRACT

This chapter describes a case of the Barchini-Knapp-Zierau transform. The transform composes well with the Penrose transform. Whereas Barchini, Knapp, and Zierau define their transform in terms of representation theory and integrals over groups, the chapter presents a geometric version. Only the simplest case, namely that for ‘hyperbolic minitwistors’ is described in detail. In this simplest case, it is just a matter of translating the representation-theoretic language. This is not so for the general case which has been worked out jointly with Leticia Barchini and Rod Gover. In general, the geometric viewpoint is an aid to proving some of the properties of the transform.