Lifts of Foliated Linear Connectionsto the Second Order Transverse Bundles
The second order transverse bundle of a foliated manifold carries a natural structure of a smooth manifold over the algebra of truncated polynomials of degree two in one variable. Prolongations of foliated mappings to second order transverse bundles are a partial case of more general -smooth foliated mappings between second order transverse bundles. We establish necessary and sufficient conditions under which a -smooth foliated diffeomorphism between two second order transverse bundles maps...