Submanifolds in the osculator bundle for the homogeneous prolongation

Abstract

Remark that the terms of the Sasaki prolongation G of a Riemannian metric has not the same physical dimensions because this prolongation is not homogeneous on the fibres of the osculator bundle OscM. This is a disavantage in the study of the geometry of OscM using the Riemannian metric determined by this prolongation. We correct this disadvantage introducing a new kind of prolongation G of the Riemannian metric, given by, which is 0-homogeneous. The geometric objects wich will be taken into consideration are recalled. Next, we find the coefficients of the induced connections.