Adapted basic connections to a certain subfoliation on the tangent manifold of a Finsler space

Abstract

On the slit tangent manifold $T{M}^0$ of a Finsler space $(M,F)$ there are given some natural foliations as vertical foliation and some other fundamental foliations produced by the vertical and horizontal Liouville vector fields, see [A. Bejancu, H. R. Farran, Finsler Geometry and Natural Foliations on the Tangent Bundle, Rep. Math. Physics 58, No. 1 (2006), 131-146]. In this paper we consider a $(n,2n-1)$-codimensional subfoliation $({\mathcal{F}}_V,{\mathcal{F}}_{\Gamma })$ on $T{M}^0$ given by vertical foliation ${\mathcal{F}}_V$ and the line foliation spanned by vertical Liouville vector field $\Gamma$ and we give a triplet of basic connections adapted to this subfoliation.