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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2020, Number 11, Pages 87–92
DOI: https://doi.org/10.26907/0021-3446-2020-11-87-92
(Mi ivm9628)
 

This article is cited in 3 scientific papers (total in 3 papers)

Brief communications

The structure of Lorentzian foliations of codimension two

N. I. Zhukova, N. G. Chebochko

National Research University Higher School of Economics, 25/12 Bolshaya Pecherskaya str., Nizhny Novgorod, 603155 Russia
Full-text PDF (357 kB) Citations (3)
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Abstract: The aim of this work is to describe the structure of complete Lorentzian foliations $(M, F)$ of codimension two on $n$-dimensional closed manifolds. It is proved that $(M, F)$ is either Riemannian or has a constant transversal curvature and its structure is described. For such foliations $(M, F)$, the criterion is obtained, reducing the chaos problem in $(M, F)$ to the same problem of the associated action of the group $O(1,1)$ on a $3$-dimensional manifold and also to the chaos problem of its global holonomy group, which is a finite-generated discrete subgroup of the isometry group of the plane with the full metric of a constant curvature.
Keywords: foliation, Lorentzian foliation, global holonomy group, Ehresmann connection.
Received: 14.09.2020
Revised: 14.09.2020
Accepted: 01.10.2020
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2020, Volume 64, Issue 11, Pages 78–82
DOI: https://doi.org/10.3103/S1066369X20110079
Bibliographic databases:
Document Type: Article
UDC: 514.7
Language: Russian
Citation: N. I. Zhukova, N. G. Chebochko, “The structure of Lorentzian foliations of codimension two”, Izv. Vyssh. Uchebn. Zaved. Mat., 2020, no. 11, 87–92; Russian Math. (Iz. VUZ), 64:11 (2020), 78–82
Citation in format AMSBIB
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\paper The structure of Lorentzian foliations of codimension two
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2020
\issue 11
\pages 87--92
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\crossref{https://doi.org/10.26907/0021-3446-2020-11-87-92}
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\jour Russian Math. (Iz. VUZ)
\yr 2020
\vol 64
\issue 11
\pages 78--82
\crossref{https://doi.org/10.3103/S1066369X20110079}
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  • https://www.mathnet.ru/eng/ivm/y2020/i11/p87
  • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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