Mathematical Research Letters

Volume 16, Issue 2, March 2009 pp. 291-301.

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

Authors: Claude LeBrun(1) and L.J. Mason (2)
Author institution: SUNY Stony Brook (1) and University of Oxford (2)

Summary: 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.

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