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Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva, 2015, Volume 17, Number 4, Pages 14–23
(Mi svmo561)
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This article is cited in 1 scientific paper (total in 1 paper)
Mathematics
Equivalent approaches to the concept of completeness of foliations
with transverse linear connection
A. Y. Dolgonsovaa, N. I. Zhukovab a Nizhny Novgorod State University of Architecture and Civil Engineering
b State University – Higher School of Economics in Nizhnii Novgorod
Abstract:
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.
Keywords:
foliation, linear conntction, Ehresmann connection, affine foliation.
Received: 11.12.2015
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Abstract page: | 52 | References: | 19 |
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