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Article

Эквивалентные подходы к понятию полноты слоений с трансверсальной линейной связностью

Долгоносова А. Ю., Жукова Н. И.

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 ane foliations
(M, F) of codimension q, q > 1, each of the mentioned above conditions are equivalent to
fulllment 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 bres of submersion onto
q -dimensional ane space.