Some natural operators on vector fields. (English) Zbl 0844.58007

Tomáš, Jiří

Arch. Math., Brno 31, No. 3, 239-249 (1995).

The paper represents a contribution to the theory of natural operators [I. Kolář, P. Michor and J. Slovák, Natural Operations in Differential Geometry, Springer-Verlag (1993; Zbl 0782.53013)]. First, all natural operators transforming vector fields on a manifold \(M\) to vector fields on \(T^* T^2 _1 M\), \(\dim M \geq 2\), are determined. Then, all natural operators transforming vector fields on \(M\) to functions on \(T^* TT^2_1 M\), \(\dim M \geq 3\), are presented. Finally, some relations between both kinds of operators are studied.

Reviewer: A.Vondra (Brno)

MSC:

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

Keywords:

natural bundle; Weil bundle; natural operators; vector fields

Citations:

Zbl 0782.53013