Prolongation of pairs of connections into connections on vertical bundles

Miroslav Doupovec and Wlodzimierz M. Mikulski

M. Doupovec, Department of Mathematics, Brno University of Technology, FSI VUT Brno, Technicka 2, 616 69 Brno, Czech Republic

W. M. Mikulski, Institute of Mathematics, Jagiellonian University, Krakow, Reymonta 4, Poland



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 I\. Kol\'a\v r and the second author on the prolongation of connections to $F$-vertical bundles. We also present some examples and applications.

AMSclassification. 58A20.

Keywords. Connection, vertical bundle.