Let (M,ℱ) be a foliated manifold. We describe all natural operators lifting ℱ-adapted (i.e. projectable in adapted coordinates) classical linear connections ∇ on (M,ℱ) into classical linear connections (∇) on the rth order adapted frame bundle .
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap93-2-4, author = {J. Kurek and W. M. Mikulski}, title = {Lifting adapted connections from foliated manifolds to higher order adapted frame bundles}, journal = {Annales Polonici Mathematici}, volume = {93}, year = {2008}, pages = {163-169}, zbl = {1137.58002}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap93-2-4} }
J. Kurek; W. M. Mikulski. Lifting adapted connections from foliated manifolds to higher order adapted frame bundles. Annales Polonici Mathematici, Tome 93 (2008) pp. 163-169. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap93-2-4/