A class of semibasic vector 1-forms on Finsler manifolds

Abstract

In this paper, we define conservative semibasic vector \(1-\)forms on the tangent bundle of a Finsler manifold. Using these vector \(1-\)forms, we characterize conservative \(L-\)Ehresmann connections with respect to the energy function. Then we find a correspondence between torsion-free semibasic vector \(1-\)forms and the subset of vertical vector fields. Taking into account this correspondence, we construct a class of semisprays that generates the Ehresmann connections mentioned above.