Geodesic
Classification of principal connections naturally induced on $W^2PE$
Archivum mathematicum, Tome 44 (2008) no. 5, pp. 535-547.

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We consider a vector bundle $E\rightarrow M$ and the principal bundle $PE$ of frames of $E$. Let $K$ be a principal connection on $PE$ and let $\Lambda $ be a linear connection on $M$. We classify all principal connections on $W^2PE= P^2M\times _M J^2PE$ naturally given by $K$ and $\Lambda $.
Classification : 53C05, 53C10, 58A20, 58A32
Keywords: natural bundle; gauge-natural bundle; natural operator; principal bundle; principal connection 
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     author = {Vondra, Jan},
     title = {Classification of principal connections naturally induced on $W^2PE$},
     journal = {Archivum mathematicum},
     pages = {535--547},
     publisher = {mathdoc},
     volume = {44},
     number = {5},
     year = {2008},
     mrnumber = {2501583},
     zbl = {1212.53040},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_2008__44_5_a13/}
}
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Vondra, Jan. Classification of principal connections naturally induced on $W^2PE$. Archivum mathematicum, Tome 44 (2008) no. 5, pp. 535-547. http://geodesic.mathdoc.fr/item/ARM_2008__44_5_a13/