Ricci identities of the Liouville d-vector fields z^2 and z^2

TL;DR

This paper introduces the theory of embeddings in the 2-osculator bundle manifold, focusing on Ricci identities of Liouville d-vector fields, and discusses submanifolds, moving frames, and covariant derivatives.

Contribution

It provides a detailed analysis of Ricci identities for Liouville d-vector fields within the context of 2-osculator bundle embeddings, extending geometric understanding.

Findings

Derivation of Ricci identities for Liouville d-vector fields

Construction of moving frames in Osc^{2}M

Analysis of induced N-linear connections

Abstract

It is the purpose of the present paper to outline an introduction in theory of embeddings in the manifold Osc^{2}M. First, we recall the notion of 2-osculator bundle. The second section is dedicated to the notion of submanifold in the total space of the 2-osculator bundle, the manifold Osc^{2}M. A moving frame is constructed. The induced N-linear connections and the relative covariant derivatives are discussed in third and fourth sections. The Ricci identities of the Liouville d-vector fields are present in the last section.