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or Minkowski Place. The values on the Levi-Civita symbol are unbiased of any metric tensor and coordinate procedure. Also, the particular phrase "image" emphasizes that it's not a tensor on account of how it transforms between coordinate techniques; nonetheless it can be interpreted for a tensor density.
These Attributes are essential for understanding the habits with the tensor in various coordinate systems.
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Using the cash pi notation Π for ordinary multiplication of quantities, an express expression for that image is:[citation essential]
but see that When the metric signature includes an odd variety of unfavorable eigenvalues q, then the signal in the parts of the tensor vary within the regular Levi-Civita symbol:
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On a pseudo-Riemannian manifold, just one could determine a coordinate-invariant covariant tensor area whose coordinate illustration agrees With all the Levi-Civita image wherever the coordinate procedure is this sort of that The premise in the tangent House is orthonormal with respect to your metric and matches a particular orientation.
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