This paper contains a classification of all affine liftings of torsion-free linear connections on n-dimensional manifolds to any linear connections on Weil bundles under the condition that n ≥ 3.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm114-1-1, author = {Jacek D\k ebecki}, title = {Affine liftings of torsion-free connections to Weil bundles}, journal = {Colloquium Mathematicae}, volume = {116}, year = {2009}, pages = {1-8}, zbl = {1166.58001}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm114-1-1} }
Jacek Dębecki. Affine liftings of torsion-free connections to Weil bundles. Colloquium Mathematicae, Tome 116 (2009) pp. 1-8. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm114-1-1/