The Structure of Lorentzian Foliations of Codimension Two

Abstract

The aim of the paper is to describe the structure of complete Lorentzian foliations $(M, F)$ of codimension two on n-dimensional closed manifolds. We prove that a foliation $(M, F)$ is either Riemannian or of constant transversal curvature and describe its structure. We obtain a criterion which reduces the chaos problem in a foliation $(M, F)$ both to the chaos problem of the smooth action of the group $O(1,1)$ on the associated locally symmetric 3-dimensional manifold and to the chaos problem of its global holonomy group, a finitely generated discrete subgroup of the isometry group of the plane with the full metric of constant curvature.