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

##### MSC:
 53C05 Connections (general theory) 58A20 Jets in global analysis
##### Keywords:
connection; jets; bundle functor; natural operator