Abstract:
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.
\Bibitem{Bel82}
\by I.~V.~Bel'ko
\paper Affine transformations of a transversal projectable connection on a foliated manifold
\jour Math. USSR-Sb.
\yr 1983
\vol 45
\issue 2
\pages 191--204
\mathnet{http://mi.mathnet.ru/eng/sm2198}
\crossref{https://doi.org/10.1070/SM1983v045n02ABEH001003}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=644768}
\zmath{https://zbmath.org/?q=an:0509.53027|0487.53026}
Linking options:
https://www.mathnet.ru/eng/sm2198
https://doi.org/10.1070/SM1983v045n02ABEH001003
https://www.mathnet.ru/eng/sm/v159/i2/p181
This publication is cited in the following 7 articles:
N. I. Zhukova, K. I. Sheina, “Gruppy bazovykh avtomorfizmov khaoticheskikh kartanovykh sloenii so svyaznostyu Eresmana”, Izvestiya vuzov. PND, 32:6 (2024), 897–907
Citation in format AMSBIB
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