ISSN 2079-6900 (Print) 
ISSN 2587-7496 (Online)

Middle Volga Mathematical Society Journal

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MSC2010 57R30

On foliations with transverse linear connection

A. Yu. Dolgonosova1

AnnotationThe subject of this article is a review of the results on foliations with transversal linear connection obtained by the author together with N.I. Zhukova, and their comparison with the results of other authors. The work consists of three parts. The first part focuses on to automorphism groups of foliations with a transversal linear connection in the category of foliations. In the second part, the question of the equivalence of the concept of completeness for the class of foliations under investigation is studied. The third part we present theorems on pseudo-Riemannian foliations that form an important class of foliations with a transversal linear connection.In particular, we present results on graphs of pseudo-Riemannian foliations that contain all information about foliations.
Keywordsfoliation, linear connection, pseudo-Riemannian foliation, graph of foliation, infinite-dimensional Lie group, Ehresmann connection, foliation with a transverse linear connection

1Anna Yu. Dolgonosova, senior lecturer of department of fundamental mathematics, research assistant of laboratory of topological methods of dynamics, National Research University Higher School of Economics (25/12 Bolshaya Pecherskay Str., Nizhny Novgorod 603155, Russia), ORCID:,

Citation: A. Yu. Dolgonosova, "[On foliations with transverse linear connection]", Zhurnal Srednevolzhskogo matematicheskogo obshchestva,19:1 (2017) 19–29 (In Russian)

DOI 10.15507/2079-6900.19.2017.01.19-29