Geodesic
Complete Lorentzian foliations of codimension 2 on closed manifolds
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Geometry, Tome 203 (2021), pp. 17-38

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In this work, we describe the structure of a complete Lorentzian foliation $(M,F)$ of codimension $2$ on an $n$-dimensional closed manifold. We prove that either $(M,F)$ is a Riemannian foliation or it has constant transverse curvature. We also describe the structure of such foliations obtain a criterion that reduces the problem of chaos in $(M,F)$ to the problem of chaos of the smooth action of the group $O(1,1)$ on the associated, locally symmetric $3$-manifold or to the problem of chaos of its global holonomy group, which is a finitely generated subgroup of the isometry group of the plane with a complete metric of constant curvature.
Mots-clés : foliation, Lorentzian foliation, chaos
Keywords: global holonomy group, Ehresmann connection. 
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     author = {N. I. Zhukova and N. G. Chebochko},
     title = {Complete {Lorentzian} foliations of codimension 2 on closed manifolds},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {17--38},
     publisher = {mathdoc},
     volume = {203},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2021_203_a2/}
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N. I. Zhukova; N. G. Chebochko. Complete Lorentzian foliations of codimension 2 on closed manifolds. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Geometry, Tome 203 (2021), pp. 17-38. http://geodesic.mathdoc.fr/item/INTO_2021_203_a2/