Vertical liouville foliations on the big-tangent manifold of a finsler space

The present paper unifies some aspects concerning the vertical Liouville distributions on the tangent (cotangent) bundle of a Finsler (Cartan) space in the context of generalized geometry. More exactly, we consider the big-tangent manifold TM associated to a Finsler space (M,F) and of its L-dual which is a Cartan space (M,K) and we define three Liouville distributions on TM which are integrable. We also find geometric properties of both leaves of Liouville distribution and the vertical distribution in our context.

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 framedf(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.

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.

On the vertical bundle of a pseudo-Finsler manifold

We define the Liouville distribution on the tangent bundle of a pseudo-Finsler manifold and prove that it is integrable. Also, we find geometric properties of both leaves of Liouville distribution and the vertical distribution.