I read some older posts about this question, but I don't know if I'm getting it. I'm working with a Lagrangian involving some Levi Civita symbols, and when I calculate a term containing ϵijk I obtain the contrary sign using ϵijk. I always apply the normal rules: ϵijk=ϵijk=1; ϵjik=ϵjik=−1 etc. I believed that there is no difference between covariant and contravariant Levi-Civita symbol. What do you know about this?
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