Let $r$, $s$, $m$, $n$, $q$ be natural numbers such that $s\ge r$. We prove that any $2$-${\mathcal{F}}\mathbb{M}_{m,n,q}$-natural operator $A\colon T_{\operatorname{2-proj}}\rightsquigarrow TJ^{(s,r)}$ transforming $2$-projectable vector fields $V$ on $(m,n,q)$-dimensional $2$-fibred manifolds $Y\rightarrow X\rightarrow M$ into vector fields $A(V)$ on the $(s,r)$-jet prolongation bundle $J^{(s,r)}Y$ is a constant multiple of the flow operator $\mathcal{J}^{(s,r)}$.
@article{108092,
author = {W\l odzimierz M. Mikulski},
title = {The jet prolongations of $2$-fibred manifolds and~the~flow~operator},
journal = {Archivum Mathematicum},
volume = {044},
year = {2008},
pages = {17-21},
zbl = {1212.58003},
mrnumber = {2431227},
language = {en},
url = {http://dml.mathdoc.fr/item/108092}
}
Mikulski, Włodzimierz M. The jet prolongations of $2$-fibred manifolds and the flow operator. Archivum Mathematicum, Tome 044 (2008) pp. 17-21. http://gdmltest.u-ga.fr/item/108092/
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