## Natural transformations of affinors into functions and affinors.(English)Zbl 0816.58002

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, 101-112 (1993).
The author’s main results can be formulated as follows:
(1) All natural transformations of affinors (i.e. tensor fields of type (1,1)) on $$n$$-dimensional manifolds into functions are of the form $$F(a_ 1(t),\dots,a_ n(t))$$, where $$a_ 1(t),\dots,a_ n(t)$$ denote the coefficients of the characteristic polynomial of the affinor $$t$$ and $$F$$ is a smooth function on $$\mathbb{R}^ n$$.
(2) All natural transformations of affinors on an $$n$$-manifold $$M$$ into $${\mathfrak H}^ 1_ 1(M)$$ are of the form $t \in {\mathfrak H}^ 1_ 1 (M) \mapsto \sum^ n_{k = 1} F_ k(a_ 1(t),\dots,a_ n(t)) t^{n- k},$ where $$F_ 1,\dots,F_ n$$ are smooth functions on $$\mathbb{R}^ n$$.
For the entire collection see [Zbl 0777.00026].

### MSC:

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

### Keywords:

natural transformations; affinors