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Fundam. Prikl. Mat., 2010, Volume 16, Issue 2, Pages 163–181 (Mi fpm1317)  

This article is cited in 1 scientific paper (total in 1 paper)

Lie jets and symmetries of prolongations of geometric objects

V. V. Shurygin

Kazan State University

Abstract: The Lie jet $\mathcal L_\theta\lambda$ of a field of geometric objects $\lambda$ on a smooth manifold $M$ with respect to a field $\theta$ of Weil $\mathbf A$-velocities is a generalization of the Lie derivative $\mathcal L_v\lambda$ of a field $\lambda$ with respect to a vector field $v$. In this paper, Lie jets $\mathcal L_\theta\lambda$ are applied to the study of $\mathbf A$-smooth diffeomorphisms on a Weil bundle $T^\mathbf AM$ of a smooth manifold $M$, which are symmetries of prolongations of geometric objects from $M$ to $T^\mathbf AM$. It is shown that vanishing of a Lie jet $\mathcal L_\theta\lambda$ is a necessary and sufficient condition for the prolongation $\lambda^\mathbf A$ of a field of geometric objects $\lambda$ to be invariant with respect to the transformation of the Weil bundle $T^\mathbf AM$ induced by the field $\theta$. The case of symmetries of prolongations of fields of geometric objects to the second-order tangent bundle $T^2M$ are considered in more detail.

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English version:
Journal of Mathematical Sciences (New York), 2011, 177:5, 758–771

Bibliographic databases:

UDC: 514.76

Citation: V. V. Shurygin, “Lie jets and symmetries of prolongations of geometric objects”, Fundam. Prikl. Mat., 16:2 (2010), 163–181; J. Math. Sci., 177:5 (2011), 758–771

Citation in format AMSBIB
\Bibitem{Shu10}
\by V.~V.~Shurygin
\paper Lie jets and symmetries of prolongations of geometric objects
\jour Fundam. Prikl. Mat.
\yr 2010
\vol 16
\issue 2
\pages 163--181
\mathnet{http://mi.mathnet.ru/fpm1317}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2786527}
\elib{https://elibrary.ru/item.asp?id=16350324}
\transl
\jour J. Math. Sci.
\yr 2011
\vol 177
\issue 5
\pages 758--771
\crossref{https://doi.org/10.1007/s10958-011-0507-3}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-80052380666}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. V. Shurygin, “Dzhety Li i chastichnye svyaznosti vysshikh poryadkov”, Materialy mezhdunarodnoi konferentsii «Geometricheskie metody v teorii upravleniya i matematicheskoi fizike: differentsialnye uravneniya, integriruemost, kachestvennaya teoriya» Ryazan, 15–18 sentyabrya 2016 g., Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 148, VINITI RAN, M., 2018, 122–129  mathnet  mathscinet
  • Фундаментальная и прикладная математика
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