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Infinitesimal affine transformations of the second order tangent bundle with horizontal lift connection

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Abstract

We obtain the canonical expansion of an infinitesimal affine transformation of the second order tangent bundle with horizontal lift connection. We establish necessary and sufficient conditions under which a vector field is an infinitesimal affine transformation. We also construct the horizontal lift of a linear connection to a second order Weil bundle.

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Authors and Affiliations

  1. Scientific and Technical Enterprise “Cryptosoft”, ul. Lermontova 3, Penza, 440026, Russia

    N. I. Manina

  2. Penza State Pedagogical University, ul. Lermontova 37, Penza, 440602, Russia

    A. Ya. Sultanov

Authors
  1. N. I. Manina
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  2. A. Ya. Sultanov
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Correspondence to N. I. Manina.

Additional information

Original Russian Text © N.I. Manina and A.Ya. Sultanov, 2011, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2011, No. 9, pp. 62–69.

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Manina, N.I., Sultanov, A.Y. Infinitesimal affine transformations of the second order tangent bundle with horizontal lift connection. Russ Math. 55, 52–57 (2011). https://doi.org/10.3103/S1066369X11090076

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  • DOI: https://doi.org/10.3103/S1066369X11090076

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