Deflection d-Tensor Identities in the Relativistic Time Dependent Lagrange Geometry

TL;DR

This paper investigates the properties of relativistic time-dependent geometric structures on jet spaces, deriving identities for connections, torsions, curvatures, and deflection tensors to deepen understanding of their interrelations.

Contribution

It introduces new identities for deflection d-tensors and explores the structure of relativistic time-dependent d-linear connections on jet spaces.

Findings

Derived Ricci and deflection tensor identities

Analyzed local components of d-linear connections, torsions, and curvatures

Enhanced understanding of geometric structures in relativistic Lagrange geometry

Abstract

The aim of this paper is to study the local components of the relativistic time dependent d-linear connections, d-torsions, d-curvatures and deflection d-tensors with respect to an adapted basis on the 1-jet space $J^{1}(R,M)$. The Ricci identities, together with their corresponding identities of deflection d-tensors, are also given.