Linear Connections on Osc^k M

Abstract

We continue the theory from the previous chapter, defining the notion of N-linear connection. In other words. we consider the linear connections which preserve by parallelism a nonlinear connection N and the k-tangent structure J. These kind of linear connections are compatible with the direct decomposition (1.1) and are very convenient for studying the geometry of total space of the k-osculator bundle Osc^k M.