The structure of Lorentzian foliations of codimension two

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.