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The covariant Levi-Civita tensor (often known as the Riemannian volume type) in almost any coordinate program that matches the chosen orientation is
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is the same old Levi-Civita image talked over in the remainder of this short article, and we employed the definition on the metric determinant in the derivation.
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The term "n-dimensional Levi-Civita image" refers to The truth that the volume of indices to the symbol n matches the dimensionality of your vector Place in query, which may be Euclidean or non-Euclidean, for example, R three displaystyle mathbb R ^ 3
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ε i j k ε l m n =
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then still left facet is zero, and right aspect is likewise zero because two of its rows are equivalent. In the same way for j c = j c + 1 displaystyle j_ c =j_ c+one