On the vertical bundle of a pseudo‐Finsler manifold

Abstract

Abstract. 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.

Contact structures on Lie algebroids

“…where the local components are expressed by Proof. 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.…”

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

“…Following [3], [9] we define two vertical Liouville distributions on T M as the complementary orthogonal distributions in V 1 and V 2 to the line distributions spanned by the Liouville vector fields E 1 and E 2 , respectively. By (1.4) and (1.5) we have…”

“…The vertical Liouville distribution on the tangent bundle of a (pseudo) Finsler space was defined for the first time in [3] where some aspects of the geometry of the vertical bundle are derived via vertical Liouville distribution. A similar study on the cotangent bundle of a Cartan space can be found in [9].…”

“…In this sense, 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). As usual, we reconsider the vertical Liouville distributions V E1 and V E2 from the case of vertical tangent (cotangent) bundle of a Finsler (Cartan) space, see [3,9], for the case of vertical subbundles V 1 and V 2 , respectively, with respect to Liouville vector fields E 1 and E 2 . Next we define the Liouville distribution V E with respect to the Liouville vector field E = E 1 + E 2 , we prove that it is integrable (Theorem 2.1) and we study some of its properties (Theorems 2.2 and 2.3).…”

Some framed f-structures on transversally Finsler foliations

“…Thus, some problems specific for tangent manifolds can be extended and studied on the normal bundle of the lifted Finsler foliation. Firstly, following [4], we define a Liouville distribution in the vertical bundle and we prove that it is integrable. Next, by analogy with [2], some framed f (3, ε)-structures on the normal bundle of the lifted Finsler foliation are defined and studied in the paper.…”