Geodesic
The natural operators lifting vector fields to generalized higher order tangent bundles
Archivum mathematicum, Tome 36 (2000) no. 3, pp. 207-212.

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For natural numbers $r$ and $n$ and a real number $a$ we construct a natural vector bundle $T^{(r),a}$ over $n$-manifolds such that $T^{(r),0}$ is the (classical) vector tangent bundle $T^{(r)}$ of order $r$. For integers $r\ge 1$ and $n\ge 3$ and a real number $a0$ we classify all natural operators $T_{\vert M_n}\rightsquigarrow TT^{(r),a}$ lifting vector fields from $n$-manifolds to $T^{(r),a}$.
Classification : 53A55, 58A20, 58A32
Keywords: natural bundle; natural transformation; natural operator 
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     author = {Mikulski, W{\l}odzimierz M.},
     title = {The natural operators lifting vector fields to generalized higher order tangent bundles},
     journal = {Archivum mathematicum},
     pages = {207--212},
     publisher = {mathdoc},
     volume = {36},
     number = {3},
     year = {2000},
     mrnumber = {1785038},
     zbl = {1049.58010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_2000__36_3_a5/}
}
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Mikulski, Włodzimierz M. The natural operators lifting vector fields to generalized higher order tangent bundles. Archivum mathematicum, Tome 36 (2000) no. 3, pp. 207-212. http://geodesic.mathdoc.fr/item/ARM_2000__36_3_a5/