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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)

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