Natural transformations of affinors into linear forms. (English) Zbl 0814.53016

Dȩbecki, Jacek

Bureš, J. (ed.) et al., The proceedings of the winter school geometry and topology, Srní, Czechoslovakia, January 1992. Palermo: Circolo Matemático di Palermo, Suppl. Rend. Circ. Mat. Palermo, II. Ser. 32, 49-59 (1994).

The author deduces that all natural transformations of affinors (i.e. tensor fields of type \((1,1)\)) into linear forms can be expressed in terms of the coefficients of the characteristic polynomial in a simple way. The proof is based on an interesting lemma, which describes all natural transformations of affinors into tensor fields of type \((2,2)\) in a similar way.
For the entire collection see [Zbl 0794.00022].

Reviewer: I.Kolář (Brno)

MSC:

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

Keywords:

natural operator; one-form; affinors; tensor fields