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Mat. Sb. (N.S.), 1982, Volume 117(159), Number 2, Pages 181–195 (Mi msb2198)  

This article is cited in 4 scientific papers (total in 4 papers)

Affine transformations of a transversal projectable connection on a foliated manifold

I. V. Bel'ko


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.

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English version:
Mathematics of the USSR-Sbornik, 1983, 45:2, 191–204

Bibliographic databases:

UDC: 514.76+515.168.3
MSC: 57S20, 57R30
Received: 17.03.1981

Citation: I. V. Bel'ko, “Affine transformations of a transversal projectable connection on a foliated manifold”, Mat. Sb. (N.S.), 117(159):2 (1982), 181–195; Math. USSR-Sb., 45:2 (1983), 191–204

Citation in format AMSBIB
\Bibitem{Bel82}
\by I.~V.~Bel'ko
\paper Affine transformations of a transversal projectable connection on a foliated manifold
\jour Mat. Sb. (N.S.)
\yr 1982
\vol 117(159)
\issue 2
\pages 181--195
\mathnet{http://mi.mathnet.ru/msb2198}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=644768}
\zmath{https://zbmath.org/?q=an:0509.53027|0487.53026}
\transl
\jour Math. USSR-Sb.
\yr 1983
\vol 45
\issue 2
\pages 191--204
\crossref{https://doi.org/10.1070/SM1983v045n02ABEH001003}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Rubanov V., “Invariant Stratifications and Transversal Connectivities”, Dokl. Akad. Nauk Belarusi, 28:8 (1984), 696–697  mathscinet  zmath  isi
    2. Zhukova N.I., “Polnye sloeniya s transversalnymi zhestkimi geometriyami i ikh bazovye avtomorfizmy”, Vestn. Rossiiskogo un-ta druzhby narodov. Ser.: Matem., inform., fiz., 2009, no. 2, 14–35  elib
    3. N.I.. Zhukova, A.Y.u. Dolgonosova, “The automorphism groups of foliations with transverse linear connection”, centr.eur.j.math, 2013  crossref  mathscinet
    4. A. Yu. Dolgonosova, “O sloeniyakh s transversalnoi lineinoi svyaznostyu”, Zhurnal SVMO, 19:1 (2017), 19–29  mathnet  crossref  elib
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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