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1936-1944
Lifting vector fields from manifolds to $r$-jet prolongation of the tangent bundle
Volume 61, no. 1 (2020), pp. 161–168

Abstract

If $m\geq 3$ and $r\geq 0$, we deduce that any natural linear operator lifting vector fields from an $m$-manifold $M$ to the $r$-jet prolongation $J^{r}TM$ of the tangent bundle $TM$ is the composition of the flow lifting $\mathcal{J}^r$ corresponding to the $r$-jet prolongation functor $J^r$ with a natural linear operator lifting vector fields from $M$ to $TM$. If $0\leq s\leq r$ and $m\geq 3$, we find all natural linear operators transforming vector fields on $M$ into base-preserving fibred maps $J^{r}TM\to J^{s}TM$.