The natural operators lifting vector fields to generalized higher order tangent bundles. (English) Zbl 1049.58010

Mikulski, Włodzimierz M.

Arch. Math., Brno 36, No. 3, 207-212 (2000).

Given an \(n\)-dimensional manifold \(M\) and \(a\in \mathbb{R}\), the author defines \(T^{r*,a}M\) to be the space of all \(r\)-jets with target zero of the local sections of the determinant bundle with weight \(a\) of \(M\). Let \(T^{(r),a}M\) be the dual vector bundle of \(T^{r*,a}M\). The author deduces that for \(a<0\), \(r\geq 1\) and \(n\geq 3\) all natural operators transforming vector fields from \(M\) to \(T^{(r),a}M\) are linearly generated (over \(\mathbb{R}\)) by the flow operator and by the Liouville vector field of the vector bundle \(T^{(r),a}M\).

Reviewer: Ivan Kolář (Brno)

MSC:

58A20	Jets in global analysis
53A55	Differential invariants (local theory), geometric objects

Keywords:

natural bundle; natural transformation; natural operator