anonanon 152k1212 gold badges233233 silver badges398398 bronze badges $endgroup$ 4 $begingroup$ That is great many thanks a bunch! I also posted an identical dilemma here: math.stackexchange.com/queries/2135276/… that You could have some insight on? $endgroup$
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RexcirusRexcirus 43544 silver badges1515 bronze badges $endgroup$ 2 $begingroup$ Your closing expression will not make A lot perception: The LHS has no cost indices $i,j,k$ While your RHS has totally free indices $i,j,l$. $endgroup$
I'm using the Einstein notation, so multiple indices are summed) or they offer two 3-indices symbols with distinct indication
The phrase "n-dimensional Levi-Civita image" refers to The point that the amount of indices within the symbol n matches the dimensionality in the vector House in query, which may be Euclidean or non-Euclidean, one example is, R three displaystyle mathbb R ^ three
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Firstly english is not really my mom tongue sorry. I need to inquire if you can help me with several of the Qualities of the levi-civita symbol.
In summary, the dialogue is with regards to the Houses with the Levi-Civita image. The main portion discusses a method that does not manage to match the expected reply, and the next component consists of proving A further formulation. The conversation finishes which has a remaining Remedy that satisfies the Attributes.
In almost any arbitrary curvilinear coordinate process and even during the absence of a metric around the manifold, the Levi-Civita symbol as defined above could be looked upon as a tensor density area in two various ways.
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For every sequence of nonempty open up sets There exists a disjoint sequence of nonempty open sets "down below" it
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Do the thing is how this can affect the value of $epsilon^ alphabetagammadelta epsilon_ alpha'beta'gamma'delta' $? $endgroup$