Natural affinors on the extended \(r\)-th order tangent bundles. (English) Zbl 0791.58009

Gancarzewicz, Jacek; Kolář, Ivan

Bureš, J. (ed.) et al., The proceedings of the 11th winter school on geometry and physics held in Srní, Czechoslovakia, January 5-12, 1991. Palermo: Circolo Matematico di Palermo, Suppl. Rend. Circ. Mat. Palermo, II. Ser. 30, 95-100 (1993).

The authors prove that all natural affinors (i.e. tensor fields of type (1,1) on the extended \(r\)-th order tangent bundle \(E^ rM\) over a manifold \(M\)) are linear combinations (the coefficients of which are smooth functions on \(\mathbb{R}\)) of four natural affinors defined in this work.
For the entire collection see [Zbl 0777.00026].

Reviewer: J.Kubarski (Łódź)

MSC:

58A30	Vector distributions (subbundles of the tangent bundles)
58A20	Jets in global analysis

Keywords:

higher order tangent bundle; natural affinors