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The Structure of Lorentzian Foliations of Codimension Two
Russian Mathematics Pub Date : 2020-12-25 , DOI: 10.3103/s1066369x20110079
N. I. Zhukova , N. G. Chebochko

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.



中文翻译:

二维余量的洛伦兹叶结构

本文的目的是描述n维封闭流形上余维二的完整洛伦兹叶面 \((M,F)\)的结构。我们证明了叶面\((M,F)\)是黎曼方程或恒定的横向曲率,并描述了其结构。我们获得一种减少了在叶理的混乱问题的标准\((M,F)\)二者的组的顺利动作的混乱问题\(O(1,1)\)在相关联的局部对称 3 -维流形及其整体整体性组的混沌问题,它是平面等距组的有限生成的离散子组,具有恒定曲率的完整度量。

更新日期:2020-12-25
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