# Article

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Keywords:
higher order cotangent bundle; natural affinor
Summary:
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.
References:
[1] Kolář, I., Modugno, M.: Torsions of connections on some natural bundles. Diff. Geom. and Appl. 2 (1992), 1-16. MR 1244453
[2] Kolář, I., Michor, P., Slovák, J.: Natural Operations in Differential Geometry. (to appear). MR 1202431
[3] Kurek, J.: Natural transformations of higher order cotangent bundles functor. to appear in Ann. Polon. Math.. MR 1215758

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