If we have a metric connection with no other restrictions (torsion may be non-zero), do the connection coefficients [itex]{\Gamma^{\alpha}}_{\mu\nu}[/itex] have any symmetries among the indeces? I'm thinking not.(adsbygoogle = window.adsbygoogle || []).push({});

Or.. for a Levi-Civita connection, the only fixed symmetry condition is [itex]{\Gamma^{\alpha}}_{\mu\nu}={\Gamma^{\alpha}}_{\nu\mu}[/itex], right? There is no relation involving the alpha index

Just wanting some confirmation. Thanks.

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# Symmetry of connection coefficients? (simple question)

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