The covariant Levi-Civita tensor (often called the Riemannian quantity sort) in almost any coordinate procedure that matches the selected orientation is

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E α β γ δ = g α ζ g β η g γ θ g δ ι E ζ η θ ι . displaystyle E^ alpha beta gamma delta =g^ alpha zeta g^ beta eta g^ gamma theta g^ delta iota E_ zeta eta theta iota ,.

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