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 $T^*\rightarrow T^{r*}$.
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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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/

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