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

##### MSC:
 58A20 Jets in global analysis 53A55 Differential invariants (local theory), geometric objects
##### Keywords:
Weil bundles; natural operators