For natural numbers $r$ and $n\geq 2$ all natural operators $T_{\vert \Cal M f_n}\rightsquigarrow T^* (J^rT^{*})$ transforming vector fields from $n$-manifolds $M$ into $1$-forms on $J^r T^{*}M=\{j^r_x (\omega)\mid \omega \in \Omega^1(M), x\in M\}$ are classified. A similar problem with fibered manifolds instead of manifolds is discussed.
@article{119346,
author = {W\l odzimierz M. Mikulski},
title = {Liftings of vector fields to $1$-forms on the $r$-jet prolongation of the cotangent bundle},
journal = {Commentationes Mathematicae Universitatis Carolinae},
volume = {43},
year = {2002},
pages = {565-573},
zbl = {1090.58005},
mrnumber = {1920532},
language = {en},
url = {http://dml.mathdoc.fr/item/119346}
}
Mikulski, Włodzimierz M. Liftings of vector fields to $1$-forms on the $r$-jet prolongation of the cotangent bundle. Commentationes Mathematicae Universitatis Carolinae, Tome 43 (2002) pp. 565-573. http://gdmltest.u-ga.fr/item/119346/
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