Informace o publikaci
The complex Goldberg-Sachs theorem in higher dimensions
Autoři | |
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Rok publikování | 2012 |
Druh | Článek v odborném periodiku |
Časopis / Zdroj | Journal of Geometry and Physics |
Fakulta / Pracoviště MU | |
Citace | |
www | http://www.sciencedirect.com/science/article/pii/S0393044012000228 |
Doi | http://dx.doi.org/10.1016/j.geomphys.2012.01.012 |
Obor | Obecná matematika |
Klíčová slova | Integrability of distributions; Null foliations; Curvature prescription; Complex geometry; Conformal geometry; Twistor geometry |
Popis | We study the geometric properties of holomorphic distributions of totally null m-planes on a (2m + epsilon)-dimensional complex Riemannian manifold (M, g), where epsilon is an element of {0, 1} and m >= 2. In particular, given such a distribution N, say, we obtain algebraic conditions on the Weyl tensor and the Cotton-York tensor which guarantee the integrability of N, and in odd dimensions, of its orthogonal complement. These results generalise the Petrov classification of the (anti-)self-dual part of the complex Weyl tensor, and the complex Goldberg-Sachs theorem from four to higher dimensions. Higher-dimensional analogues of the Petrov type D condition are defined, and we show that these lead to the integrability of up to 2(m) holomorphic distributions of totally null m-planes. Finally, we adapt these findings to the category of real smooth pseudo-Riemannian manifolds, commenting notably on the applications to Hermitian geometry and Robinson (or optical) geometry. |
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