# zbMATH — the first resource for mathematics

Natural operators transforming projectable vector fields to product preserving bundles. (English) Zbl 0959.58001
Slovák, Jan (ed.) et al., Proceedings of the 18th winter school “Geometry and physics”, Srní, Czech Republic, January 10-17, 1998. Palermo: Circolo Matematico di Palermo, Suppl. Rend. Circ. Mat. Palermo, II. Ser. 59, 181-187 (1999).
Let $$Y\to M$$ be a fibered manifold over a manifold $$M$$ and $$\mu: A\to B$$ be a homomorphism between Weil algebras $$A$$ and $$B$$. Using the results of Mikulski and others, which classify product preserving bundle functors on the category of fibered manifolds, the author classifies all natural operators $$T_{\text{proj}} Y\to T^\mu Y$$, where $$T_{\text{proj}}Y$$ denotes the space of projective vector fields on $$Y$$ and $$T^\mu$$ the bundle functors associated with $$\mu$$.
For the entire collection see [Zbl 0913.00039].

##### MSC:
 58A05 Differentiable manifolds, foundations 58A20 Jets in global analysis
##### Keywords:
natural operators; projective vector fields