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Keywords:
$(s,r)$-jet; bundle functor; natural operator; flow operator; $2$-fibred manifold; $2$-projectable vector field
$(s,r)$-jet; bundle functor; natural operator; flow operator; $2$-fibred manifold; $2$-projectable vector field
Summary:
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 $\mathcal{J}^{(s,r)}$.
References:
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[3] Mikulski, W. M.: The jet prolongations of fibered manifolds and the flow operator. Publ. Math. Debrecen 59 (2001), 441–458. MR 1874443
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