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Ricci and Bianchi identities for h -normal Γ -linear connections on J 1 ( T , M )

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  • Mircea Neagu

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 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 .

Suggested Citation

  • Mircea Neagu, 2003. "Ricci and Bianchi identities for h -normal Γ -linear connections on J 1 ( T , M )," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2003, pages 1-15, January.
    • Handle: RePEc:hin:jijmms:412587
    DOI: 10.1155/S0161171203012419
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