Local Bianchi Identities in the Relativistic Non-Autonomous Lagrange Geometry

The aim of this paper is to describe the local Bianchi identities for an $h$-normal $\mathrm{\Gamma }$-linear connection of Cartan type $\mathrm{\nabla }\mathrm{\Gamma }$ 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 $\mathrm{\nabla }\mathrm{\Gamma }$ and we give the general local expressions of Bianchi identities which connect these d-torsions and d-curvatures.