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ISSN (Print) 2079-6900

ISSN (Online) 2587-7496

(Middle Volga Mathematical Society Journal)

Scientific Journal

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

A. Yu. Dolgonosova1, N. I. Zhukova2

AnnotationWe 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.
Keywordsfoliation, 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)