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

Abstract

On the slit tangent manifold TM0 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 (FV,FG) on TM0 given by vertical foliation FV and the line foliation spanned by vertical Liouville vector field G and we give a triplet of basic connections adapted to this subfoliation.