Geodesic
Prolongation of second order connections to vertical Weil bundles
Archivum mathematicum, Tome 37 (2001) no. 4, pp. 333-347

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We study systematically the prolongation of second order connections in the sense of C. Ehresmann from a fibered manifold into its vertical bundle determined by a Weil algebra $A$. In certain situations we deduce new properties of the prolongation of first order connections. Our original tool is a general concept of a $B$-field for another Weil algebra $B$ and of its $A$-prolongation.
Classification : 53C05, 58A20, 58A32
Keywords: non-holonomic jet; Weil bundle; Weil field; second order connection; prolongation of connections 
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     author = {Cabras, Antonella and Kol\'a\v{r}, Ivan},
     title = {Prolongation of second order connections to vertical {Weil} bundles},
     journal = {Archivum mathematicum},
     pages = {333--347},
     publisher = {mathdoc},
     volume = {37},
     number = {4},
     year = {2001},
     mrnumber = {1879456},
     zbl = {1090.58003},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_2001__37_4_a9/}
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Cabras, Antonella; Kolář, Ivan. Prolongation of second order connections to vertical Weil bundles. Archivum mathematicum, Tome 37 (2001) no. 4, pp. 333-347. http://geodesic.mathdoc.fr/item/ARM_2001__37_4_a9/