Natural liftings of vector fields to tangent bundles of bundles of 1- forms. (English) Zbl 0743.53008

Kobak, Piotr

Math. Bohem. 116, No. 3, 319-326 (1991).

The author determines all natural operators transforming vector fields on a manifold \(M\) into vector fields on \(T(T^*M)\), \(\dim M\geq 2\). All of them are generated by five simple constructions which are based on the prolongation of the flow of a vector field and on the generalized Liouville vector field of an arbitrary vector bundle.

Reviewer: I.Kolář (Brno)

MSC:

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

Keywords:

natural operators; vector fields; prolongation of the flow