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  1. Christoffel Symbols

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    Christoffel Symbols of the First Kind
    A related set of quantities, the Christoffel Symbols of the First Kind (${\Gamma_{\rho\mu\nu}}$), are defined by lowering the upper index using the metric tensor:
    $${\Gamma{\rho\mu\nu}} = g{\rho\sigma} \Gamma^{\sigma}{}_{\mu\nu}$$