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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
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
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
Linking options:
https://www.mathnet.ru/eng/ivm9628 https://www.mathnet.ru/eng/ivm/y2020/i11/p87
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Abstract page: | 124 | Full-text PDF : | 41 | References: | 16 | First page: | 1 |
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