On Some Transverse Geometrical Structures of Lifted Foliation to Its Conormal Bundle

We consider the lift of a foliation to its conormal bundle and some transverse geometrical structures associated with this foliation are studied. We introduce a good vertical connection on the conormal bundle and, moreover, if the conormal bundle is endowed with a transversal Cartan metric, we obtain that the lifted foliation to its conormal bundle is a Riemannian one. Also, some transversally framed f(3, ε)-structures of corank 2 on the normal bundle of lifted foliation to its conormal bundle are introduced and an almost (para)contact structure on a transverse Liouville distribution is obtained.