Lifting adapted connections from foliated manifolds to higher order adapted frame bundles
Tom 93 / 2008
Annales Polonici Mathematici 93 (2008), 163-169 MSC: Primary 58A20. DOI: 10.4064/ap93-2-4
Let $(M,\mathcal F)$ be a foliated manifold. We describe all natural operators $\mathcal A$ lifting $\mathcal F$-adapted (i.e. projectable in adapted coordinates) classical linear connections $\nabla$ on $(M,\mathcal F)$ into classical linear connections $\mathcal A(\nabla)$ on the $r$th order adapted frame bundle $P^r(M,\mathcal F)$.