The complex Goldberg-Sachs theorem in higher dimensions

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

The complex Goldberg-Sachs theorem in higher dimensions

Popis výsledku v původním jazyce

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 &gt;= 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.

Název v anglickém jazyce

The complex Goldberg-Sachs theorem in higher dimensions

Popis výsledku anglicky

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 &gt;= 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.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

—

Návaznosti

V - Vyzkumna aktivita podporovana z jinych verejnych zdroju

Rok uplatnění

2012

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Journal of Geometry and Physics

ISSN

0393-0440

e-ISSN

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Svazek periodika

62

Číslo periodika v rámci svazku

5

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

32

Strana od-do

981-1012

Kód UT WoS článku

000302527300005

EID výsledku v databázi Scopus

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