One studies the flow prolongation of projectable vector fields with respect to a bundle functor of order on the category of fibered manifolds. As a result, one constructs an operator transforming connections on a fibered manifold into connections on an arbitrary vertical bundle over . It is deduced that this operator is the only natural one of finite order and one presents a condition on vertical bundles over under which every natural operator in question has finite order.
@article{701652,
title = {Natural lifting of connections to vertical bundles},
booktitle = {Proceedings of the 19th Winter School "Geometry and Physics"},
series = {GDML\_Books},
publisher = {Circolo Matematico di Palermo},
address = {Palermo},
year = {2000},
pages = {97-102},
mrnumber = {MR1758084},
zbl = {0978.53056},
url = {http://dml.mathdoc.fr/item/701652}
}
Kolář, Ivan; Mikulski, Włodzimierz M. Natural lifting of connections to vertical bundles, dans Proceedings of the 19th Winter School "Geometry and Physics", GDML_Books, (2000), pp. 97-102. http://gdmltest.u-ga.fr/item/701652/