Geodesic
Liftings of $1$-forms to the linear $r$-tangent bundle
Archivum mathematicum, Tome 31 (1995) no. 2, pp. 97-111

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Let $r,n$ be fixed natural numbers. We prove that for $n$-manifolds the set of all linear natural operators $T^*\rightarrow T^*T^{(r)}$ is a finitely dimensional vector space over $R$. We construct explicitly the bases of the vector spaces. As a corollary we find all linear natural operators $T^*\rightarrow T^{r*}$.
Classification : 53A55, 58A20
Keywords: linear r-tangent bundle; linear natural operator; 1-form 
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     author = {Mikulski, W. M.},
     title = {Liftings of $1$-forms to the linear $r$-tangent bundle},
     journal = {Archivum mathematicum},
     pages = {97--111},
     publisher = {mathdoc},
     volume = {31},
     number = {2},
     year = {1995},
     mrnumber = {1357978},
     zbl = {0844.58006},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_1995__31_2_a1/}
}
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Mikulski, W. M. Liftings of $1$-forms to the linear $r$-tangent bundle. Archivum mathematicum, Tome 31 (1995) no. 2, pp. 97-111. http://geodesic.mathdoc.fr/item/ARM_1995__31_2_a1/