Duke Mathematical Journal

Nonlinear gravitons, null geodesics, and holomorphic disks

Claude Lebrun and L. J. Mason

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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 S2×S2, 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 CP3 with boundary on some totally real embedding of RP3 into CP3. 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

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Duke Math. J., Volume 136, Number 2 (2007), 205-273.

First available in Project Euclid: 21 December 2006

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Zentralblatt MATH identifier

Primary: 53C28: Twistor methods [See also 32L25] 83C60: Spinor and twistor methods; Newman-Penrose formalism
Secondary: 14D21: Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory) [See also 32L25, 81Txx]


Lebrun, Claude; Mason, L. J. Nonlinear gravitons, null geodesics, and holomorphic disks. Duke Math. J. 136 (2007), no. 2, 205--273. doi:10.1215/S0012-7094-07-13621-4. https://projecteuclid.org/euclid.dmj/1166711369

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