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In this paper we study some problems related to a vertical Liouvilledistribution (called vertical Liouville-Hamilton distribution) on the cotangentbundle of a Cartan space. We study the existence of some linear connections ofVr\u{a}nceanu type on Cartan spaces related to some foliated structures. Also,we identify a certain $(n,2n-1)$--codimensional subfoliation$(\mathcal{F}_V,\mathcal{F}_{C^*})$ on $T^*M_0$ given by vertical foliation$\mathcal{F}_V$ and the line foliation $\mathcal{F}_{C^*}$ spanned by thevertical Liouville-Hamilton vector field $C^*$ and we give a triplet of basicconnections adapted to this subfoliation. Finally, using the vertical Liouvillefoliation $\mathcal{F}_{V_{C^*}}$ and the natural almost complex structure on$T^*M_0$ we study some aspects concerning the cohomology of $c$--indicatrixcotangent bundle.

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