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Lie Jets and Higher-Order Partial Connections

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Abstract

Higher-order partial connections are studied. We find conditions under which the Lie jet of a field of a geometric object ξ in the direction of the field of Weil 𝔸-velocities Y coincides with the covariant derivative ∇Yξ of this field with respect to some higher-order partial connection.

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Authors and Affiliations

  1. Kazan’ (Volga Region) Federal University, Kazan’, Russia

    V. V. Shurygin

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  1. V. V. Shurygin
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Correspondence to V. V. Shurygin.

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Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 148, Proceedings of the International Conference “Geometric Methods in Control Theory and Mathematical Physics: Differential Equations, Integrability, and Qualitative Theory” (Ryazan, September 15–18, 2016), 2018.

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Shurygin, V.V. Lie Jets and Higher-Order Partial Connections. J Math Sci 248, 497–504 (2020). https://doi.org/10.1007/s10958-020-04890-2

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