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ε i j k ε l m n =
I am utilizing the Einstein notation, so several indices are summed) or they offer two 3-indices symbols with unique indication
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first of all english is not really my mom tongue sorry. I want to ask If you're able to enable me with a lot of the Attributes with the levi-civita symbol.
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Using the money pi notation Π for normal multiplication of quantities, an explicit expression for that symbol is:[citation essential]
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E α β γ δ E ρ σ μ ν = − g α ζ g β η g γ θ g δ ι δ ρ σ μ ν ζ η θ ι E α β γ δ E ρ σ μ ν = − g α ζ g β η g γ θ g δ ι δ ζ η θ ι ρ σ μ ν E α β γ δ E α β γ δ = − 24 E α β γ δ E ρ β γ δ = − 6 δ ρ α E α β γ δ E ρ σ γ δ = − two δ ρ σ α β E α β γ δ E ρ σ θ δ = − δ ρ σ θ α β γ . displaystyle commence aligned E_ alpha beta gamma delta E_ rho sigma mu nu &=-g_ alpha zeta g_ beta eta g_ gamma theta g_ delta iota delta _ rho sigma mu nu ^ zeta eta theta iota E^ alpha beta gamma delta E^ rho sigma mu nu &=-g^ alpha zeta g^ beta eta g^ gamma theta g^ delta iota delta _ zeta eta theta iota ^ rho sigma mu nu E^ alpha beta gamma delta E_ alpha beta gamma delta &=-24E^ alpha beta gamma delta E_ rho beta gamma delta &=-sixdelta _ rho ^ alpha E^ alpha beta gamma delta E_ rho sigma gamma delta &=-2delta _ rho sigma ^ check here alpha beta E^ alpha beta gamma delta E_ rho sigma theta delta &=-delta _ rho sigma theta ^ alpha beta gamma ,.conclusion aligned
exactly where gab will be the representation with the metric in that coordinate system. We will equally take into account a contravariant Levi-Civita tensor by elevating the indices Along with the metric as typical,
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