Mathematical Research Letters

Volume 16 (2009)

Number 2

The Einstein-Weyl Equations, Scattering Maps, and Holomorphic Disks

Pages: 291 – 301

DOI: http://dx.doi.org/10.4310/MRL.2009.v16.n2.a7

Authors

Claude LeBrun (SUNY Stony Brook)

L. J. Mason (University of Oxford)

Abstract

We show that conformally compact, space-time oriented, globally hyperbolic, Lorentzian Einstein-Weyl $3$-manifolds are in natural one-to-one correspondence with orientation-reversing diffeomorphisms of the complex projective line. The proof hinges on a holomorphic-disk analog of Hitchin’s mini-twistor correspondence.

Full Text (PDF format)