1985/01/01 by Michael G. Eastwood · 1 citation
Mathematics · #Mathematics and Applications #Point processes and geometric inequalities
paper · doi:10.1017/s030500410006271x
openalex publication_date 1985/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/05/21
The Penrose transform is an integral geometric method of interpreting elements of various analytic cohomology groups on open subsets of complex projective 3-space as solutions of linear differential equations on the Grassmannian of 2-planes in 4-space. The motivation for such a transform comes from interpreting this Grassmannian as the complexification of the conformal compactification of Minkowski space, the differential equations being the massless field equations of various helicities. This transform is a cornerstone of twistor theory [22, 24, 30], but the methods generalize considerably as will be explained in this article. Closely related is the Ward correspondence [28], a non-linear version of a special case of the Penrose transform. It also admits a rather more general treatment. The object of this article is to explain the general case and the natural connection between the Penrose and Ward approaches.