%0 Journal Article
%T Wave equations and the LeBrun-Mason correspondence
%A Fuminori Nakata
%J Mathematics
%D 2009
%I arXiv
%X The LeBrun-Mason twistor correspondences for $S^1$-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.
%U http://arxiv.org/abs/0907.0928v2