Geodesic
The structure of Lorentzian foliations of codimension two
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 11 (2020), pp. 87-92

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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.
Mots-clés : foliation, Lorentzian foliation
Keywords: global holonomy group, Ehresmann connection. 
@article{IVM_2020_11_a6,
     author = {N. I. Zhukova and N. G. Chebochko},
     title = {The structure of {Lorentzian} foliations of codimension two},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {87--92},
     publisher = {mathdoc},
     number = {11},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2020_11_a6/}
}
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N. I. Zhukova; N. G. Chebochko. The structure of Lorentzian foliations of codimension two. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 11 (2020), pp. 87-92. http://geodesic.mathdoc.fr/item/IVM_2020_11_a6/