Nonlinear gravitons, null geodesics, and holomorphic disks

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 S 2 × S 2 , there is an infinite-dimensional moduli space of such conformal structures,...

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Veröffentlicht in:Duke mathematical journal 2007-02, Vol.136 (2), p.205-273
Hauptverfasser: Lebrun, Claude, Mason, L. J.
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Mason, L. J.
description 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 S 2 × S 2 , 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 C P 3 with boundary on some totally real embedding of R P 3 into C P 3 . 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
doi_str_mv 10.1215/S0012-7094-07-13621-4
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subjects 14D21
53C28
81Txx
83C60
Applications of vector bundles and moduli spaces in mathematical physics (twistor theory
instantons
Newman-Penrose formalism
quantum field theory) [See also 32L25
Spinor and twistor methods
Twistor methods [See also 32L25]
title Nonlinear gravitons, null geodesics, and holomorphic disks
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