Natural operators on vector fields on the cotangent bundles of the bundles of \((k,r)\)-velocities. (English) Zbl 0929.58001

Tomáš, Jiří

Slovák, Jan (ed.) et al., Proceedings of the 17th winter school “Geometry and physics”, Srní, Czech Republic, January 11–18, 1997. Palermo: Circolo Matematico di Palermo, Suppl. Rend. Circ. Mat. Palermo, II. Ser. 54, 113-124 (1998).

Let \(T^AM\) be the bundle of \(A\)-points of a manifold \(M\) for a Weil algebra \(A\). The author investigates the problem of the classification of all natural operators \(T\to TT^*T^A\) for a Weil algebra \(A\). In fact, the author classifies all natural operators \(T_M\to TT^*T^r_kM\) for \(\dim M\geq k+2\) and gives their geometric descriptions, where \(T^r_kM\) denotes the bundle of \((k,r)\)-velocities of \(M\).
For the entire collection see [Zbl 0904.00040].

Reviewer: A.Morimoto (Nagoya)

MSC:

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

Keywords:

Weil bundles; natural operators