The complex Goldberg-Sachs theorem in higher dimensions

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F12%3A00064684" target="_blank" >RIV/00216224:14310/12:00064684 - isvavai.cz</a>
Result on the web
<a href="http://www.sciencedirect.com/science/article/pii/S0393044012000228" target="_blank" >http://www.sciencedirect.com/science/article/pii/S0393044012000228</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.geomphys.2012.01.012" target="_blank" >10.1016/j.geomphys.2012.01.012</a>

Result language
angličtina
Original language name
The complex Goldberg-Sachs theorem in higher dimensions
Original language description
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 partof 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.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Publication year
2012
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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