N-Linear Connections Structure Equations

Abstract

The theory presented in the previous chapter is very useful in the study of the geometry of total space of an osculator bundle E = Osc ² M. Thus, the direct decomposition (5.1), Ch.2, allows to decompose the tensor fields on E or on Ẽ in the components, with respect to the distributions N _o, N ₁, V _2. But these components are special tensor fields, called distinguished tensor fields. In the geometry of the manifold E we have determined the so-called distinguished vector fields or covector fields. The coordinates of d-vectors or d-covectors have the same rules of transformations as those of the vector or covector fields on the base manifold M. Similar considerations can be done for the notion of linear connection on E.