Nonlinear Gravitons, Null Geodesics, and Holomorphic Disks
LeBrun, Claude ; Mason, L. J.
arXiv, 0504582 / Harvested from arXiv
Text on arXiv
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 x 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 CP_3 with boundary on some totally real embedding of RP^3 into CP_3. An interesting sub-class of these conformal structures are represented by scalar-flat indefinite K\"ahler metrics, and our methods give particularly sharp results in this more restrictive setting.
Publié le : 2005-04-28
Classification:  Mathematics - Differential Geometry,  General Relativity and Quantum Cosmology,  High Energy Physics - Theory,  Mathematical Physics,  Mathematics - Complex Variables,  53C50,  32L25,  32G10,  14J30 
@article{0504582,
     author = {LeBrun, Claude and Mason, L. J.},
     title = {Nonlinear Gravitons, Null Geodesics, and Holomorphic Disks},
     journal = {arXiv},
     volume = {2005},
     number = {0},
     year = {2005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0504582}
}

LeBrun, Claude; Mason, L. J. Nonlinear Gravitons, Null Geodesics, and Holomorphic Disks. arXiv, Tome 2005 (2005) no. 0, . http://gdmltest.u-ga.fr/item/0504582/