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or Minkowski House. The values of your Levi-Civita image are independent of any metric tensor and coordinate process. Also, the specific phrase "image" emphasizes that it's not a tensor thanks to how it transforms concerning coordinate techniques; nevertheless it could be interpreted as being a tensor density.
Examples of Levi-Civita properties in 4 Proportions consist of the symmetric and antisymmetric character in the tensor, its relation to your metric tensor, and its transformation Attributes below coordinate transformations.
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but notice that When the metric signature includes an odd variety of detrimental eigenvalues q, then the indicator from the parts of this tensor vary from the standard Levi-Civita image:
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The covariant Levi-Civita tensor (also known as the Riemannian volume form) in almost any coordinate method that matches the chosen orientation is
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