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1. Christoffel Symbols

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   Christoffel Symbols of the Third Kind (Historical Note)
   Historically, a set termed the Christoffel Symbols of the Third Kind (${\Gamma^{\rho}_{\mu\nu\sigma}}$) were proposed by Cartan in 1927, defined as the symbols multiplied by the metric tensor in a specific manner intended to capture intrinsic torsion before the Levi-Civita connection formalized the torsion-free requirement. These symbols are now largely obsolete, primarily remai…