Abstract
We develop a global twistor correspondence for pseudo-Riemannian conformal structures of signature with self-dual Weyl curvature. Near the conformal class of the standard indefinite product metric on , there is an infinite-dimensional moduli space of such conformal structures, and each of these has the surprising global property that its null geodesics are all periodic. Each such conformal structure arises from a family of holomorphic disks in with boundary on some totally real embedding of into . Some of these conformal classes are represented by scalar-flat indefinite Kähler metrics, and our methods give particularly sharp results in connection with this special case
Citation
Claude Lebrun. L. J. Mason. "Nonlinear gravitons, null geodesics, and holomorphic disks." Duke Math. J. 136 (2) 205 - 273, 01 February 2007. https://doi.org/10.1215/S0012-7094-07-13621-4
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