Mathematical Research Letters

Volume 16 (2009)

Number 2

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

Pages: 291 – 301



Claude LeBrun (SUNY Stony Brook)

L. J. Mason (University of Oxford)


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.

Published 1 January 2009