Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2018, Volume 148, Pages 122–129 (Mi into310)  
Lie Jets and Higher-Order Partial Connections

V. V. Shurygin

Kazan (Volga Region) Federal University
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Abstract: Higher-order partial connections are studied in the paper. We find conditions under which the Lie jet of the field of a geometric object $\xi$ in the direction of the field of Weil $\mathbb{A}$-velocities $Y$ coincides with the covariant derivative $\nabla_Y\xi$ of this field with respect to some higher-order partial connection.
Keywords: Weil algebra, Weil bundle, partial connection, higher-order connection, Lie derivative, Lie jet.
English version:
Journal of Mathematical Sciences (New York), 2020, Volume 248, Issue 4, Pages 497–504
DOI: https://doi.org/10.1007/s10958-020-04890-2
Bibliographic databases:
Document Type: Article
UDC: 514.763
MSC: 53C15, 58A20, 58A32
Language: Russian
Citation: V. V. Shurygin, “Lie Jets and Higher-Order Partial Connections”, Proceedings of the International Conference “Geometric Methods in Control Theory and Mathematical Physics: Differential Equations, Integrability, and Qualitative Theory,” Ryazan, September 15–18, 2016, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 148, VINITI, M., 2018, 122–129; J. Math. Sci. (N. Y.), 248:4 (2020), 497–504
Citation in format AMSBIB
\Bibitem{Shu18}
\by V.~V.~Shurygin
\paper Lie Jets and Higher-Order Partial Connections
\inbook Proceedings of the International Conference ``Geometric Methods in Control Theory and Mathematical Physics: Differential Equations, Integrability, and Qualitative Theory,'' Ryazan, September 15--18, 2016
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2018
\vol 148
\pages 122--129
\publ VINITI
\publaddr M.
\mathnet{http://mi.mathnet.ru/into310}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3847715}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2020
\vol 248
\issue 4
\pages 497--504
\crossref{https://doi.org/10.1007/s10958-020-04890-2}
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