### Equivalent approaches to the concept of completeness of foliations with transverse linear connection

#### A. Yu. Dolgonosova1, N. I. Zhukova2

Annotation We prove the equivalence of three different approaches to the definition of completeness of a foliation with transverse linear connection. It is shown that for the transverse affine foliations $(M, F)$ of codimension $q, \, q \geqslant 1,$ each of the mentioned above conditions are equivalent to fulfillment of the following two conditions: 1) there exists an Ehresmann connection to $(M, F)$; 2) the induced foliation on the universal covering space is formed by fibres of submersion onto $q$-dimensional affine space. foliation, linear conntction, Ehresmann connection, affine foliation

1Lecturer of department of scientific disciplines, Nizhny Novgorod State University of Architecture and Civil Engineering, Nizhny Novgorod; annadolgonosova@gmail.com

2Professor of department of fundamental mathematics, National Research University Higher School of Economics, Nizhny Novgorod; nzhukova@hse.ru

Citation: A. Yu. Dolgonosova, N. I. Zhukova, "[Equivalent approaches to the concept of completeness of foliations with transverse linear connection]", Zhurnal Srednevolzhskogo matematicheskogo obshchestva,17:4 (2015) 14–23 (In Russian)