For a linear r-th order connection on the tangent bundle we characterize geometrically its integrability in the sense of the theory of higher order G-structures. Our main tool is a bijection between these connections and the principal connections on the r-th order frame bundle and the comparison of the torsions under both approaches.
@article{bwmeta1.element.doi-10_2478_BF02475215,
author = {Ivan Kol\'a\v r},
title = {On the torsion of linear higher order connections},
journal = {Open Mathematics},
volume = {1},
year = {2003},
pages = {360-366},
zbl = {1045.53015},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_BF02475215}
}
Ivan Kolář. On the torsion of linear higher order connections. Open Mathematics, Tome 1 (2003) pp. 360-366. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_BF02475215/
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