A de Rham theorem with respect to the Liouville foliation on TM^0, for a Finsler manifold M

TL;DR

This paper introduces new vertical forms related to the Liouville foliation on the slit tangent bundle of a Finsler manifold, establishing a de Rham theorem for the associated cohomology group.

Contribution

It defines new types of vertical forms and proves a de Rham theorem for the cohomology of TM^0 with respect to the Liouville foliation.

Findings

Defined new vertical forms on TM^0

Established a de Rham type theorem for the cohomology group

Provided a cohomological framework for Liouville foliation

Abstract

On the slit tangent manifold of a Finsler manifold M are given the vertical and the Liouville foliations. In this paper we define some new types of vertical forms with respect to the Liouville foliation on TM^0. We define a cohomology group of TM^0 using these new forms. We prove a de Rham type theorem.