Gauss-Weingarten and Frenet equations in the theory of the homo- geneous lift to the 2-osculator bundle of a Finsler metric

Abstract

In this article, we present a study of the subspaces of the manifold Osc²M, the total space of the 2-osculator bundle of a real manifold M. We obtain the induced connections of the canonical N-linear metric connection determined by the homogeneous prolongation of a Finsler metric to the manifold ^Osc2M. We present the Gauss-Weingarten equations of the associated 2-osculator submanifold. We construct a Frenet frame and we determine the Frenet equations of a curve from the manifold Osc²M.