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Kazan. Gos. Univ. Uchen. Zap. Ser. Fiz.-Mat. Nauki, 2009, Volume 151, Book 4, Pages 36–50 (Mi uzku764)  

This article is cited in 2 scientific papers (total in 2 papers)

Holomorphic Tensor Fields and Linear Connections on a Second Order Tangent Bundle

F. R. Gainullina, V. V. Shuryginb

a "Itplus" Ltd.
b Chair of Geometry, Kazan State University

Abstract: The second order tangent bundle $T^2M$ of a smooth manifold $M$ carries a natural structure of a smooth manifold over the algebra $\mathbf R(\varepsilon^2)$ of truncated polynomials of degree 2. A section $\sigma$ of $T^2M$ induces an $\mathbf R(\varepsilon^2)$-smooth diffeomorphism $\Sigma\colon T^2M\to T^2M$. Conditions are obtained under which an $\mathbf R(\varepsilon^2)$-smooth tensor field and an $\mathbf R(\varepsilon^2)$-smooth linear connection on $T^2M$ can be transfered by a diffeomorphism of the form $\Sigma$, respectively, into the lift of a tensor field and the lift of a linear connection given on $M$.

Keywords: tangent bundle of second order, lift of a linear connection, lift of a tensor field, holomorphic connection, Lie derivative.

Full text: PDF file (281 kB)
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UDC: 514.76
Received: 30.07.2009

Citation: F. R. Gainullin, V. V. Shurygin, “Holomorphic Tensor Fields and Linear Connections on a Second Order Tangent Bundle”, Kazan. Gos. Univ. Uchen. Zap. Ser. Fiz.-Mat. Nauki, 151, no. 4, Kazan University, Kazan, 2009, 36–50

Citation in format AMSBIB
\Bibitem{GaiShu09}
\by F.~R.~Gainullin, V.~V.~Shurygin
\paper Holomorphic Tensor Fields and Linear Connections on a~Second Order Tangent Bundle
\serial Kazan. Gos. Univ. Uchen. Zap. Ser. Fiz.-Mat. Nauki
\yr 2009
\vol 151
\issue 4
\pages 36--50
\publ Kazan University
\publaddr Kazan
\mathnet{http://mi.mathnet.ru/uzku764}


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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, “Lie jets and symmetries of prolongations of geometric objects”, J. Math. Sci., 177:5 (2011), 758–771  mathnet  crossref  mathscinet  elib
    2. A. Ya. Sultanov, O. A. Monakhova, “Affinnye preobrazovaniya v rassloeniyakh”, Geometriya, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 146, VINITI RAN, M., 2018, 48–88  mathnet  mathscinet
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