Geodesic
Natural affinors on higher order cotangent bundle
Archivum mathematicum, Tome 28 (1992) no. 3-4, pp. 175-180.

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All natural affinors on the $r$-th order cotangent bundle $T^{r*}M$ are determined. Basic affinors of this type are the identity affinor id of $TT^{r*}M$ and the $s$-th power affinors $Q^s_M : TT^{r*}M \rightarrow VT^{r*}M$ with $s=1, \dots , r$ defined by the $s$-th power transformations $A^{r,r}_s$ of $T^{r*}M$. An arbitrary natural affinor is a linear combination of the basic ones.
Classification : 53A55, 58A20
Keywords: higher order cotangent bundle; natural affinor 
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     author = {Kurek, Jan},
     title = {Natural affinors on higher order cotangent bundle},
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Kurek, Jan. Natural affinors on higher order cotangent bundle. Archivum mathematicum, Tome 28 (1992) no. 3-4, pp. 175-180. http://geodesic.mathdoc.fr/item/ARM_1992__28_3-4_a4/