Local Bianchi Identities in the Relativistic Non-Autonomous Lagrange Geometry

TL;DR

This paper derives local Bianchi identities for a specific type of linear connection on jet spaces, detailing the relations between torsion and curvature tensors in relativistic non-autonomous Lagrange geometry.

Contribution

It provides explicit local expressions for Bianchi identities associated with h-normal Γ-linear connections of Cartan type on jet spaces, advancing geometric understanding.

Findings

Explicit formulas for torsion and curvature components.

Derived local Bianchi identities connecting torsion and curvature.

Enhanced geometric framework for relativistic non-autonomous Lagrange spaces.

Abstract

The aim of this paper is to describe the local Bianchi identities for an $h$-normal $\Gamma$-linear connection of Cartan type $\nabla\Gamma$ on the first-order jet space $J^1(R,M)$. In this direction, we present the local expressions of the adapted components of the torsion and curvature d-tensors produced by $\nabla\Gamma$ and we give the general local expressions of Bianchi identities which connect these d-torsions and d-curvatures.