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Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva, 2015, Volume 17, Number 4, Pages 14–23 (Mi svmo561)  

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
Citations (1)
References:
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
Bibliographic databases:
UDC: 514.7
Language: Russian
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  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva
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