The natural affinors on some fiber product preserving gauge bundle functors of vector bundles. (English) Zbl 1164.58302

Kurek, Jan; Mikulski, Włodzimierz M.

Arch. Math., Brno 42, No. 1, 59-67 (2006).

Let \(\mathcal V\mathcal B_m\) be the category of vector bundles over \(m\)-dimensional manifolds and linear morphisms with local diffeomorphisms as base maps. In [Ann.Pol.Math.82, 251-264 (2003; Zbl 1126.58300)], the second author described all fiber product preserving gauge bundle functors on \(\mathcal V\mathcal B_m\). Using the methods developed in that paper, the authors determine all natural tensor fields of type \((1,1)\) on a vertical fiber product preserving gauge bundle functor on \(\mathcal V\mathcal B_m\). Certain concrete examples are discussed in detail.

Reviewer: Ivan Kolář (Brno)

MSC:

58A05	Differentiable manifolds, foundations
58A20	Jets in global analysis

Keywords:

natural operators; natural transformations; natural affinors; jets

Citations:

Zbl 1126.58300