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

Abstract

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 T M 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 T M which are integrable. We also find geometric properties of both leaves of Liouville distribution and the vertical distribution in our context.

Contact structures on Lie algebroids

“…Follows using an argument similar to that used in [4,22]. It can be found in [23] for a more general case when the manifold M is endowed with a Finsler structure.…”

“…Let us begin by considering a vertical Liouville distribution on T M as the complementary orthogonal distribution in V to the line distribution spanned by the unitary Liouville vector field ξ 2 = 1 √ F 2 +K 2 E. In [23] this distribution is considered in a more general case when the manifold M is endowed with a Finsler structure and for this reason certain proofs are omitted here.…”