On the $k$-Semispray of Nonlinear Connections in $k$-Tangent Bundle Geometry

TL;DR

This paper introduces a method to generate sequences of $k$-semisprays and nonlinear connections on the $k$-tangent bundle, with special cases for Lagrange and Finsler spaces of order $k$.

Contribution

It provides a novel systematic approach to construct sequences of $k$-semisprays and nonlinear connections in $k$-tangent bundle geometry.

Findings

Sequences of $k$-semisprays and nonlinear connections can be derived from a given structure.

Special cases include Lagrange and Finsler spaces of order $k$.

The method enhances understanding of geometric structures in higher-order tangent bundles.

Abstract

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 $k$.