anonanon 152k1212 gold badges233233 silver badges398398 bronze badges $endgroup$ 4 $begingroup$ That is best many thanks a bunch! I also posted an analogous question right here: math.stackexchange.com/queries/2135276/… that You may have some insight on? $endgroup$
The Levi-Civita image is most often Utilized in three and four dimensions, also to some extent in two Proportions, so these are typically supplied below in advance of defining the final scenario. Two Proportions[edit]
RexcirusRexcirus 43544 silver badges1515 bronze badges $endgroup$ 2 $begingroup$ Your final expression doesn't make A great deal feeling: The LHS has absolutely free indices $i,j,k$ While your RHS has free indices $i,j,l$. $endgroup$
or Minkowski Area. The values on the Levi-Civita symbol are impartial of any metric tensor and coordinate process. Also, the specific time period "symbol" emphasizes that it is not a tensor as a result of how it transforms involving coordinate methods; however it can be interpreted as being a tensor density.
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The Levi-Civita tensor is Employed in the Einstein field equations to specific the curvature of spacetime with regards to the Electrical power and momentum of issue and radiation.
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The covariant Levi-Civita tensor (also known as the Riemannian volume sort) in almost any coordinate method that matches the selected orientation is
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