An integral transform on a cylinder and the twistor correspondence

2012/01/17 by Nakata, Fuminori
#32G10 #35L05 #53C28 #53C50 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1201.3450

Abstract

Twistor correspondences for R-invariant indefinite self-dual conformal structures on R⁴ 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.

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