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

2013/01/22 by Adelina Manea, Manea, Adelina, Cristian Ida +1 · 1 citation
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #math.DG

paper · pdf · doi:10.48550/arxiv.1301.5275

arxiv created 2013/01/22 · arxiv updated 2013/01/23

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 (F_V,F_Γ) on TM⁰ given by vertical foliation F_V and the line foliation spanned by vertical Liouville vector field Γ and we give a triplet of basic connections adapted to this subfoliation.

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