Wave equations and the LeBrun-Mason correspondence

2009/07/06 by Fuminori Nakata, Nakata, Fuminori
Mathematics · #32G10 #35L05 #53C28 #53C50 #Advanced Mathematical Physics Problems #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.0907.0928

openalex publication_date 2009/07/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The LeBrun-Mason twistor correspondences for S¹-invariant self-dual Zollfrei metrics are explicitly established. We give explicit formulas for the general solutions of the wave equation and the monopole equation on the de Sitter three-space under the assumption for the tameness at infinity by using Radon-type integral transforms, and the above twistor correspondence is described by using these formulas. We also obtain a critical condition for the LeBrun-Mason twistor spaces, and show that the twistor theory does not work well for twistor spaces which do not satisfy this condition.

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