Lorentzian manifolds with shearfree congruences and Kahler-Sasaki geometry

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F62690094%3A18470%2F21%3A50018387" target="_blank" >RIV/62690094:18470/21:50018387 - isvavai.cz</a>

Výsledek na webu

<a href="https://www.sciencedirect.com/science/article/pii/S0926224521000085?via%3Dihub" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0926224521000085?via%3Dihub</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.difgeo.2021.101724" target="_blank" >10.1016/j.difgeo.2021.101724</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Lorentzian manifolds with shearfree congruences and Kahler-Sasaki geometry

Popis výsledku v původním jazyce

We study Lorentzian manifolds (M, g) of dimension n &gt;= 4, equipped with a maximally twisting shearfree null vector field p, for which the leaf space S=M/{exptp} is a smooth manifold. If n = 2k, the quotient S = M/{exptp} is naturally equipped with a subconformal structure of contact type and, in the most interesting cases, it is a regular Sasaki manifold projecting onto a quantisable Kahler manifold of real dimension 2k - 2. Going backwards through this line of ideas, for any quantisable Kahler manifold with associated Sasaki manifold S, we give the local description of all Lorentzian metrics g on the total spaces M of A-bundles pi : M -&gt; S, A = S-1, R, such that the generator of the group action is a maximally twisting shearfree g-null vector field p. We also prove that on any such Lorentzian manifold (M, g) there exists a non-trivial generalised electromagnetic plane wave having pas propagating direction field, a result that can be considered as a generalisation of the classical 4-dimensional Robinson Theorem. We finally construct a 2-parametric family of Einstein metrics on a trivial bundle M = R x S for any prescribed value of the Einstein constant. If dim M = 4, the Ricci flat metrics obtained in this way are the well-known Taub-NUT metrics. (C) 2021 Elsevier B.V. All rights reserved.

Název v anglickém jazyce

Lorentzian manifolds with shearfree congruences and Kahler-Sasaki geometry

Popis výsledku anglicky

We study Lorentzian manifolds (M, g) of dimension n &gt;= 4, equipped with a maximally twisting shearfree null vector field p, for which the leaf space S=M/{exptp} is a smooth manifold. If n = 2k, the quotient S = M/{exptp} is naturally equipped with a subconformal structure of contact type and, in the most interesting cases, it is a regular Sasaki manifold projecting onto a quantisable Kahler manifold of real dimension 2k - 2. Going backwards through this line of ideas, for any quantisable Kahler manifold with associated Sasaki manifold S, we give the local description of all Lorentzian metrics g on the total spaces M of A-bundles pi : M -&gt; S, A = S-1, R, such that the generator of the group action is a maximally twisting shearfree g-null vector field p. We also prove that on any such Lorentzian manifold (M, g) there exists a non-trivial generalised electromagnetic plane wave having pas propagating direction field, a result that can be considered as a generalisation of the classical 4-dimensional Robinson Theorem. We finally construct a 2-parametric family of Einstein metrics on a trivial bundle M = R x S for any prescribed value of the Einstein constant. If dim M = 4, the Ricci flat metrics obtained in this way are the well-known Taub-NUT metrics. (C) 2021 Elsevier B.V. All rights reserved.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GA18-00496S" target="_blank" >GA18-00496S: Singulární prostory ze speciální holonomie a foliací</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2021

Kód důvěrnosti údajů

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

Název periodika

DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS

ISSN

0926-2245

e-ISSN

—

Svazek periodika

75

Číslo periodika v rámci svazku

April

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

32

Strana od-do

"Article Number: 101724"

Kód UT WoS článku

000632451300011

EID výsledku v databázi Scopus

2-s2.0-85100743702