anonanon 152k1212 gold badges233233 silver badges398398 bronze badges $endgroup$ 4 $begingroup$ Which is fantastic many thanks a bunch! I also posted an analogous concern right here: math.stackexchange.com/inquiries/2135276/… that you might have some insight on? $endgroup$
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RexcirusRexcirus 43544 silver badges1515 bronze badges $endgroup$ 2 $begingroup$ Your ultimate expression does not make A great deal sense: The LHS has free indices $i,j,k$ While your RHS has free indices $i,j,l$. $endgroup$
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Examples of Levi-Civita Houses in four Proportions include the symmetric and antisymmetric character on the tensor, its relation for the metric tensor, and its transformation Attributes beneath coordinate transformations.
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Sure, there are still several open inquiries and regions of exploration relevant to Levi-Civita Attributes in four Proportions.
For starters english is not my mother tongue sorry. I desire to request If you're able to aid me with several of the Qualities of the levi-civita symbol.
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The subsequent are examples of the overall identity earlier mentioned specialized to Minkowski Room (Along with the unfavorable indication arising from your odd variety of negatives from the signature from the metric tensor in either signal Conference):
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These include things like additional being familiar with the geometric and Bodily implications of those properties, in addition to their feasible generalizations to increased Proportions and also other mathematical constructions.
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The covariant Levi-Civita tensor (often known as the Riemannian volume kind) in any coordinate method that matches the selected orientation is
the place gab would be the representation of the metric in that coordinate system. We can easily in the same way look at a contravariant Levi-Civita tensor by increasing the indices With all the metric as typical,
Do you see how this can affect the worth of $epsilon^ alphabetagammadelta epsilon_ alpha'beta'gamma'delta' $? $endgroup$