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Sibirskii Matematicheskii Zhurnal, 2024, Volume 65, Number 6, Pages 1115–1127
DOI: https://doi.org/10.33048/smzh.2024.65.605 (Mi smj7913) 		 
Extremals of the induced sub-Lorentz structure on the Gödel universe

V. N. Berestovskii

Sobolev Institute of Mathematics, Novosibirsk, Russia
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DOI: https://doi.org/10.33048/smzh.2024.65.605
Abstract: We study the Gödel universe as the Lie group with the induced left-invariant sub-Lorentz structure defined by some proper subspace of the Lie algebra that generates it. We find the expressions for timelike and isotropic extremals in elementary functions by methods of geometric optimal control. Also, we prove that these extremals are not closed but as a rule not complete, having proper open subintervals of the real line as maximal connected domains.
Keywords: Gödel universe, induced left-invariant sub-Lorentz structure, isotropic extremal, Lie algebra, Lie group, orthonormal basis, timelike extremal.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation FWNF-2022-0006
The work was carried out in the framework of the State Task to the Sobolev Institute of Mathematics (Project FWNF-2022–0006).
Received: 16.05.2024
Revised: 10.07.2024
Accepted: 20.08.2024
English version:
Siberian Mathematical Journal, 2024, Volume 65, Issue 6, Pages 1292–1304
DOI: https://doi.org/10.1134/S0037446624060053
Document Type: Article
UDC: 514.82+512.81+517.977
MSC: 35R30
Language: Russian
Citation: V. N. Berestovskii, “Extremals of the induced sub-Lorentz structure on the Gödel universe”, Sibirsk. Mat. Zh., 65:6 (2024), 1115–1127; Siberian Math. J., 65:6 (2024), 1292–1304
Citation in format AMSBIB
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\by V.~N.~Berestovskii
\paper Extremals of the induced sub-Lorentz structure on the G\"odel universe
\jour Sibirsk. Mat. Zh.
\yr 2024
\vol 65
\issue 6
\pages 1115--1127
\mathnet{http://mi.mathnet.ru/smj7913}
\crossref{https://doi.org/10.33048/smzh.2024.65.605}
\transl
\jour Siberian Math. J.
\yr 2024
\vol 65
\issue 6
\pages 1292--1304
\crossref{https://doi.org/10.1134/S0037446624060053}
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