Let $F$ be a natural bundle. We introduce the geometrical construction transforming two general connections into a general connection on the $F$-vertical bundle. Then we determine all natural operators of this type and we generalize the result by IK̇olář and the second author on the prolongation of connections to $F$-vertical bundles. We also present some examples and applications.
@article{107970,
author = {Miroslav Doupovec and W\l odzimierz M. Mikulski},
title = {Prolongation of pairs of connections into connections on vertical bundles},
journal = {Archivum Mathematicum},
volume = {041},
year = {2005},
pages = {409-422},
zbl = {1112.58003},
mrnumber = {2195494},
language = {en},
url = {http://dml.mathdoc.fr/item/107970}
}
Doupovec, Miroslav; Mikulski, Włodzimierz M. Prolongation of pairs of connections into connections on vertical bundles. Archivum Mathematicum, Tome 041 (2005) pp. 409-422. http://gdmltest.u-ga.fr/item/107970/
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