Geodesic
The natural operators lifting vector fields to $(J\sp rT\sp *)\sp *$
Archivum mathematicum, Tome 36 (2000) no. 4, pp. 255-260.

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For integers $r\ge 2$ and $n\ge 2$ a complete classification of all natural operators $A:T_{\vert M_n}\rightsquigarrow T(J^rT^*)^*$ lifting vector fields to vector fields on the natural bundle $(J^rT^*)^*$ dual to $r$-jet prolongation $J^rT^*$ of the cotangent bundle over $n$-manifolds is given.
Classification : 53A55, 58A20, 58A32
Keywords: bundle functors; natural transformations; natural operators 
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     author = {Mikulski, W{\l}odzimierz M.},
     title = {The natural operators lifting vector fields to $(J\sp rT\sp *)\sp *$},
     journal = {Archivum mathematicum},
     pages = {255--260},
     publisher = {mathdoc},
     volume = {36},
     number = {4},
     year = {2000},
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     zbl = {1049.58011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_2000__36_4_a1/}
}
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Mikulski, Włodzimierz M. The natural operators lifting vector fields to $(J\sp rT\sp *)\sp *$. Archivum mathematicum, Tome 36 (2000) no. 4, pp. 255-260. http://geodesic.mathdoc.fr/item/ARM_2000__36_4_a1/