An integral transform on a cylinder and the twistor correspondence

TL;DR

This paper develops an explicit integral transform-based twistor correspondence for certain indefinite self-dual conformal structures on R^4, connecting functions on a cylinder to those on Lorentz space, and summarizes general twistor construction methods.

Contribution

It introduces a natural integral transform for twistor correspondence on a cylinder and summarizes a general method for constructing indefinite self-dual and Einstein-Weyl spaces.

Findings

Explicit twistor correspondence for R-invariant indefinite self-dual structures.

Connection between the integral transform and wave equation, Radon transform.

Summary of general twistor construction methods for indefinite spaces.

Abstract

Twistor correspondences for R-invariant indefinite self-dual conformal structures on R^4 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 R^{1,2} 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.