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 |
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| container_title | Duke mathematical journal |
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| creator | Lebrun, Claude 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 |
| format | Article |
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| ispartof | Duke mathematical journal, 2007-02, Vol.136 (2), p.205-273 |
| issn | 0012-7094 1547-7398 |
| language | eng |
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| source | Project Euclid Complete |
| 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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