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Some natural constructions on vector fields and higher order cotangent bundles. (English) Zbl 0796.58002
Let \(T^{r*} M=J^ r (M,R)_ 0\) be the bundle of all \(r\)-th order velocities on an \(n\)-dimensional manifold \(M\). First of all, the author determines all natural operators transforming vector fields on \(M\) into vector fields on \(T^{r*} M\), provided \(n \geq 3\). This complicated problem is solved by means of an original technique, which is developed in the paper. Such a technique is also used for finding all natural operators transforming vector fields on \(M\) into base preserving morphisms \(T^{q*} M \to T^{r*} M\).
Reviewer: I.Kolář (Brno)

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