Geodesic
The jet prolongations of $2$-fibred manifolds and the flow operator
Archivum mathematicum, Tome 44 (2008) no. 1, pp. 17-21 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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 $\mathcal{J}^{(s,r)}$.
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 $\mathcal{J}^{(s,r)}$.
Classification : 58A20
Keywords: $(s, r)$-jet; bundle functor; natural operator; flow operator; $2$-fibred manifold; $2$-projectable vector field 
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     title = {The jet prolongations of $2$-fibred manifolds and~the~flow~operator},
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}
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Mikulski, Włodzimierz M. The jet prolongations of $2$-fibred manifolds and the flow operator. Archivum mathematicum, Tome 44 (2008) no. 1, pp. 17-21. http://geodesic.mathdoc.fr/item/ARM_2008_44_1_a2/

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