Nonlinear connections on 2-jet bundle J2(T, M)

Abstract

The aim of this paper is to introduce the main geometrical objects on the 2-jet bundle J²(T, M), which is the natural extension of the 1-jet bundle J¹(T, M): In this direction, we firstly introduce the geometrical concept of a nonlinear connection N on the 2-jet space J²(T, M), in order to construct the adapted bases of vector and covector fields. Then, we describe the Lie brackets of the d-vector fields of the adapted basis of vector fields.