Natural lifting of connections to vertical bundles. (English) Zbl 0978.53056

Kolář, Ivan; Mikulski, Włodzimierz M.

Slovák, Jan (ed.) et al., The proceedings of the 19th Winter School “Geometry and physics”, Srní, Czech Republic, January 9-15, 1999. Palermo: Circolo Matematico di Palermo, Suppl. Rend. Circ. Mat. Palermo, II. Ser. 63, 97-102 (2000).

One studies the flow prolongation of projectable vector fields with respect to a bundle functor of order \((r,s,q)\) on the category of fibered manifolds. As a result, one constructs an operator transforming connections on a fibered manifold \(Y\) into connections on an arbitrary vertical bundle over \(Y\). It is deduced that this operator is the only natural one of finite order and one presents a condition on vertical bundles over \(Y\) under which every natural operator in question has finite order.
For the entire collection see [Zbl 0940.00040].

Reviewer: M.Anastasiei (Iaşi)

MSC:

53C05	Connections (general theory)
58A20	Jets in global analysis

Keywords:

connection; jets; bundle functor; natural operator