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The term "n-dimensional Levi-Civita image" refers to The point that the volume of indices on the image n matches the dimensionality with the vector Place in concern, which may be Euclidean or non-Euclidean, for example, R three displaystyle mathbb R ^ three
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but detect that if the metric signature contains an odd number of destructive eigenvalues q, then the indication with the factors of the tensor vary with the common Levi-Civita symbol:[9]
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is the standard Levi-Civita image mentioned in the rest of this information, and we utilized the definition with the metric determinant in the derivation.
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