Sasakian structure on the unit tangent bundle of a Finsler manifold

Abstract

In this work, we introduce an adopted local frame on the tangent bundle of a Finsler manifold with respect to the natural foliations of the tangent bundle. We show the prominence of using this local frame by studying some geometric properties of the foliations and distributions on the tangent bundle of a Finsler manifold. Moreover, we find the necessary and sufficient conditions on the Finsler manifold ( M, F ) such that the unit tangent bundle admits a Sasakian structure.