Upon h-normal \Gamma-linear connections on J^1(T,M) (original) (raw)

The aim of this paper is to describe the local Ricci and Bianchi identities of an hnormal Γ -linear connection on the first-order jet fibre bundle J 1 (T , M). We present the physical and geometrical motives that determined our study and introduce the h-normal Γ -linear connections on J 1 (T , M), emphasizing their particular local features. We describe the expressions of the local components of torsion and curvature d-tensors produced by an h-normal Γ -linear connection ∇Γ , and analyze the local Ricci identities induced by ∇Γ , together with their derived local deflection d-tensors identities. Finally, we expose the local expressions of Bianchi identities which geometrically connect the local torsion and curvature d-tensors of connection ∇Γ .