The jet prolongations of \(2\)-fibred manifolds and the flow operator. (English) Zbl 1212.58003

Mikulski, Włodzimierz M.

Arch. Math., Brno 44, No. 1, 17-21 (2008).

Summary: Let \(r, s, m, n\) and \(q\) be natural numbers such that \(s\geq r\). We prove that any \(2\)-\({\mathcal F}{\mathcal M}_{m,n,q}\) -natural operator \(A\: T_{2-\text{proj} }\rightsquigarrow TJ^{(s,r)}\) transforming \(2\)-projectable vector fields \(V\) on \((m,n,q)\)-dimensional \(2\)-fibred manifolds \(Y\to X\to M\) into vector fields \(A(V)\) on the \((s,r)\)-jet prolongation bundle \(J^{(s,r)}Y\) is a constant multiple of the flow operator \(\mathcal J^{(s,r)}\).

MSC:

58A20

Jets in global analysis

Keywords:

\((s,r)\)-jet; bundle functor; natural operator; flow operator; \(2\)-fibred manifold; \(2\)-projectable vector field