Geodesic
Affine transformations of a transversal projectable connection on a foliated manifold
Sbornik. Mathematics, Tome 45 (1983) no. 2, pp. 191-204

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Consider the principal bundle of quotient-frames on a foliated manifold. This paper gives, and supplements, results about canonical, transversal and projectable forms, about foliated vector fields and their natural lifts, and about lifted foliations. The basic cross-sections of a transversal connection are introduced and studied. Criteria for transversality and projectability of connections in the quotient-frame bundle are established, and it is shown that the quotient Lie algebra consisting of the infinitesimal affine transformations of a projectable connection is finite-dimensional, and that so is the quotient Lie group consisting of affine transformations of a transversally-complete, projectable connection on a manifold with a transversally orientable foliation having a closed leaf. Bibliography: 19 titles. 
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     author = {I. V. Bel'ko},
     title = {Affine transformations of a transversal projectable connection on a foliated manifold},
     journal = {Sbornik. Mathematics},
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     number = {2},
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     url = {http://geodesic.mathdoc.fr/item/SM_1983_45_2_a2/}
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I. V. Bel'ko. Affine transformations of a transversal projectable connection on a foliated manifold. Sbornik. Mathematics, Tome 45 (1983) no. 2, pp. 191-204. http://geodesic.mathdoc.fr/item/SM_1983_45_2_a2/