Some natural constructions on vector fields and higher order cotangent bundles (Q1321533)

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 \(T^{q*} M \to T^{r*} M\).