Article
Ufa Mathematical Journal
Volume 14, Number 1, pp. 20-36
The structure of foliations with integrable Ehresmann connection
Sheina K.I., Zhukova N.I.
DOI:10.13108/2022-14-1-20
Download PDF
Article on MathNetAbstact
We study foliations of arbitrary codimension $q$ on $n$-dimensional smooth manifolds admitting an integrable Ehresmann
connection. The category of such foliations is considered, where isomorphisms preserve both
foliations and their Ehresman connections. We show that this category can be considered as that of bifoliations covered by products. We introduce the notion of a canonical bifoliation and we prove that each
foliation $(M, F)$ with integrable Ehresmann connection is isomorphic to some canonical bifoliation.
A category of triples is constructed and we prove that it is equivalent to
the category of foliations with integrable Ehresmann connection. In this way, the classification of foliations
with integrable Ehresman connection is reduced to the classification of associated diagonal actions of discrete
groups of diffeomorphisms of the product of manifolds. The classes of foliations with integrable Ehresmann connection
are indicated. The application to $G$-foliations is considered.