On the $k$-Semispray of Nonlinear Connections in $k$-Tangent Bundle   Geometry
  In this paper we present a method by which is obtained a sequence of $k$-semisprays and two sequences of nonlinear connections on the $k$-tangent bundle $T^kM$, starting from a given one. Interesting particular cases appear for Lagrange and Finsler spaces of order $k$. 
Florian Munteanu
math.DG