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## Main Question or Discussion Point

hi, I have seen some examples related to christoffel symbol when it was symmetric, but I have not seen any anti symmetric christoffel symbol examples. For instance, in torsion tensor, if we have anti symmetric christoffel symbol, torsion tensor does not vanish. To sum up, in what kind of situations is christoffel symbol anti symmetric and in what kind of situations does torsion tensor remain?? Could you please give some examples??