anonanon 152k1212 gold badges233233 silver badges398398 bronze badges $endgroup$ 4 $begingroup$ That is great many thanks a bunch! I also posted a similar query listed here: math.stackexchange.com/issues/2135276/… that you might have some insight on? $endgroup$

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RexcirusRexcirus 43544 silver badges1515 bronze badges $endgroup$ 2 $begingroup$ Your final expression isn't going to make Significantly feeling: The LHS has cost-free indices $i,j,k$ Whilst your RHS has free indices $i,j,l$. $endgroup$

ε i j ε i n = δ j n displaystyle varepsilon _ ij varepsilon ^ in = delta _ j ^ n

These Qualities are important for being familiar with the conduct from the tensor in several coordinate techniques.

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then still left facet is zero, and proper facet is additionally zero since two of its rows are equivalent. Equally for j c = j c + 1 displaystyle j_ c =j_ c+1

The Levi-Civita tensor is used in the Einstein area equations to precise the curvature of spacetime with regards to the Electrical power and momentum of issue and radiation.

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On a pseudo-Riemannian manifold, just one could determine a coordinate-invariant covariant tensor discipline whose coordinate representation agrees Along with the Levi-Civita symbol anywhere the coordinate system is these kinds of that The premise in the tangent House is orthonormal with respect on the metric and matches a selected orientation.

wherever gab is the representation on the metric in that coordinate process. We can likewise take into account a contravariant Levi-Civita tensor by boosting the indices Using the metric as normal,

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