TRANSVERSELY ANALYTICAL LORENTZIAN FOLIATIONS OF CODIMENSION TWO 

Bagaev Andrey Vladimirovich, Candidate of physical and mathematical sciences, associate professor, sub-department of applied mathematics, Nizhny Novgorod State Technical University named after R.E. Alekseev (24 Minina street, Nizhny Novgorod, Russia), a.v.bagaev@gmail.com
Zhukova Nina Ivanovna, Doctor of physical and mathematical sciences, associate professor, subdepartment of fundamental mathematics, National Research University “Higher School of Economics” (25/12 Bolshaya Pecherskaya street, Nizhny Novgorod, Russia), nina.i.zhukova@yandex.ru

514.7

10.21685/2072-3040-2017-4-3

Background. The Lorentzian geometry is radically different from the Riemannian geometry and finds widespread application in various physical theories. The goal of this work is to investigate the structure of transversely analytical Lorentzian foliations (M, F) of codimension two on n-dimensional manifolds.
Methods. The methods of foliated bundles and holonomy pseudogroups are applied.
Results. We prove a criterion for Lorentzian foliations of codimension two with Ehresmann connection to be Riemannian. A description of the structure of transversely analytical non-Riemannian Lorentzian foliations of codimension two is given.
Conclusions. Any transversely analytical Lorentzian foliation of codimension two with an Ehresmann connection is either a Riemannian and has the structure of one of the following types: 1) all leaves are closed and the leaf space is a smooth orbifold; 2) closures of leaves form a Riemannian foliation of codimension one, each leaf of which is a minimal set; 3) each leaf is dense everywhere; or its transversely Gaussian curvature is constant and it is covered by the trivial fibration  L₀ x R² → R² , where L₀  is a manifold diffeomorphic to any leaf without holonomy.

Lorentzian foliation, Ehresmann connection, germ holonomy group of a leaf

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