An integral transform on a cylinder and the twistor correspondence

Details An integral transform on a cylinder and the twistor correspondence An integral transform on a cylinder and the twistor correspondence

2012-01-17

arxiv.org/abs/1201.3450v1

Mathematics

Differential Geometry

15 pages

Scientific paper

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.

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