Geodesic
Infinitesimal affine transformations of the second order tangent bundle with horizontal lift connection
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 9 (2011), pp. 62-69

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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 orderWeil bundle.
Keywords: second order tangent bundle, linear connection, horizontal lift of a linear connection, second order Weil bundle.
Mots-clés : infinitesimal affine transformation 
@article{IVM_2011_9_a6,
     author = {N. I. Manina and A. Ya. Sultanov},
     title = {Infinitesimal affine transformations of the second order tangent bundle with horizontal lift connection},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {62--69},
     publisher = {mathdoc},
     number = {9},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2011_9_a6/}
}
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N. I. Manina; A. Ya. Sultanov. Infinitesimal affine transformations of the second order tangent bundle with horizontal lift connection. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 9 (2011), pp. 62-69. http://geodesic.mathdoc.fr/item/IVM_2011_9_a6/