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.
@article{107811,
author = {Antonella Cabras and Ivan Kol\'a\v r},
title = {Prolongation of second order connections to vertical Weil bundles},
journal = {Archivum Mathematicum},
volume = {037},
year = {2001},
pages = {333-347},
zbl = {1090.58003},
mrnumber = {1879456},
language = {en},
url = {http://dml.mathdoc.fr/item/107811}
}
Cabras, Antonella; Kolář, Ivan. Prolongation of second order connections to vertical Weil bundles. Archivum Mathematicum, Tome 037 (2001) pp. 333-347. http://gdmltest.u-ga.fr/item/107811/
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