The Gauss-Weingarten formulae for the homogeneous lift to the osculator bundle of a Finsler metric

Abstract

In this article, we present a study of the subspaces of the manifold OscM, the total space of the osculator bundle of a real manifold M.We obtain the induced connections of the canonical metrical N-linear connection determined by the homogeneous prolongation of a Finsler metric to the manifold OscM. We present the Gauss-Weingarten equations of the associated osculator submanifold.