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 $T^*\rightarrow T^{r*}$.
@article{107530,
author = {W\l odzimierz M. Mikulski},
title = {Liftings of $1$-forms to the linear $r$-tangent bundle},
journal = {Archivum Mathematicum},
volume = {031},
year = {1995},
pages = {97-111},
zbl = {0844.58006},
mrnumber = {1357978},
language = {en},
url = {http://dml.mathdoc.fr/item/107530}
}
Mikulski, Włodzimierz M. Liftings of $1$-forms to the linear $r$-tangent bundle. Archivum Mathematicum, Tome 031 (1995) pp. 97-111. http://gdmltest.u-ga.fr/item/107530/
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