Ricci identities of the Liouville d-vector fields z^(1)alpha and z^(2)alpha

TL;DR

This paper explores the Ricci identities related to Liouville d-vector fields within the context of 2-osculator bundles, providing foundational concepts and geometric structures in the theory of embeddings.

Contribution

It introduces the Ricci identities of Liouville d-vector fields on 2-osculator bundles and discusses associated geometric structures and covariant derivatives.

Findings

Derived Ricci identities for Liouville d-vector fields.

Constructed moving frames and discussed induced connections.

Provided foundational framework for embeddings in Osc^{2}M.

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.