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

Abstract

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 Vrȃnceanu type on Cartan spaces related to some foliated structures. Also, we identify a certain (n, 2n − 1)codimensional subfoliation (F V , F C * ) on T * M 0 given by vertical foliation F V and the line foliation F C * 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 F V C * and the natural almost complex structure on T * M 0 we study some aspects concerning the cohomology of c-indicatrix cotangent bundle.

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

“…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]. Also, other signifiant studies concerning the interrelations between natural foliations defined by Liouville fields on the tangent bundle of a Finsler space and the geometry of the Finsler space itself, as well as similar problems on Cartan spaces are intensively studied in [5] and [1], respectively.…”

“…Also, other signifiant studies concerning the interrelations between natural foliations defined by Liouville fields on the tangent bundle of a Finsler space and the geometry of the Finsler space itself, as well as similar problems on Cartan spaces are intensively studied in [5] and [1], respectively. See also [9,11,16,17].…”

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.…”

Geometrical structures on the cotangent bundle

“…The paper is organized as follows. In the first section we present the preliminary results on the cotangent bundle (see for instance [13,[19][20][21]28]). Also, we study the tension and the strong torsion of the nonlinear connection and investigate the homogeneous case.…”

“…show us the relation between the Jacobi endomorphism given by(13) and curvature tensor from(2).We recall that the pair (T * M, ω) is a symplectic manifold. Every differentiable function f : T * M → R determines an unique vector field X f on T * M called the 1650071-7 Int.…”