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International Journal of Mathematics and Mathematical Sciences
Volume 2003, Issue 34, Pages 2177-2191
http://dx.doi.org/10.1155/S0161171203012419

Ricci and Bianchi identities for h-normal Γ-linear connections on J1(T,M)

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Received 14 March 2001; Revised 1 November 2001

Copyright © 2003 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The aim of this paper is to describe the local Ricci and Bianchi identities of an h-normal Γ-linear connection on the first-order jet fibre bundle J1(T,M). We present the physical and geometrical motives that determined our study and introduce the h-normal Γ-linear connections on J1(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.