Geodesic
Prolongation of pairs of connections into connections on vertical bundles
Archivum mathematicum, Tome 41 (2005) no. 4, pp. 409-422.

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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.
Classification : 53C05, 58A20, 58A32
Keywords: connection; vertical bundle 
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     author = {Doupovec, Miroslav and Mikulski, W{\l}odzimierz M.},
     title = {Prolongation of pairs of connections into connections on vertical bundles},
     journal = {Archivum mathematicum},
     pages = {409--422},
     publisher = {mathdoc},
     volume = {41},
     number = {4},
     year = {2005},
     mrnumber = {2195494},
     zbl = {1112.58003},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_2005__41_4_a5/}
}
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Doupovec, Miroslav; Mikulski, Włodzimierz M. Prolongation of pairs of connections into connections on vertical bundles. Archivum mathematicum, Tome 41 (2005) no. 4, pp. 409-422. http://geodesic.mathdoc.fr/item/ARM_2005__41_4_a5/