The Einstein-Weyl Equations, Scattering Maps, and Holomorphic Disks
Differential Geometry
2008-07-25 v2 General Relativity and Quantum Cosmology
Complex Variables
Symplectic Geometry
Abstract
We show that conformally compact, globally hyperbolic, Lorentzian Einstein-Weyl 3-manifolds are in natural one-to-one correspondence with orientation-reversing diffeomorphisms of the 2-sphere. The proof hinges on a holomorphic-disk analog of Hitchin's mini-twistor correspondence.
Cite
@article{arxiv.0806.3761,
title = {The Einstein-Weyl Equations, Scattering Maps, and Holomorphic Disks},
author = {Claude LeBrun and L. J. Mason},
journal= {arXiv preprint arXiv:0806.3761},
year = {2008}
}
Comments
11 pages, LaTeX2e. Revised version strengthens result and completes proof