A vertical Liouville subfoliation on the cotangent bundle of a Cartan space and some related structures

In this paper, we study some problems related to a vertical Liouville distribution (called vertical Liouville–Hamilton distribution) on the cotangent bundle of a Cartan space. We study the existence of some linear connections of Vrănceanu type on Cartan spaces related to some foliated structures. Also, we identify a certain (n, 2n-1)-codimensional subfoliation [Formula: see text] on T*M0given by vertical foliation [Formula: see text] and the line foliation [Formula: see text] spanned by the vertical Liouville–Hamilton vector field C* and we give a triplet of basic connections adapted to this subfoliation. Finally, using the vertical Liouville foliation [Formula: see text] and the natural almost complex structure on T*M0we study some aspects concerning the cohomology of c-indicatrix cotangent bundle.