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Assume that $T_{ijkl}$ is a 4-th rank isotropic tensor. Why is it $\epsilon_{ijk}T_{ijkl}=0$, without assuming the general formula for a 4-th rank isotropic tensor $\alpha \delta_{ij}\delta_{kl}+\beta\delta_{ik}\delta_{jl}+\gamma\delta_{il}\delta_{jk}$?

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Just a hint, both $T$ and $\epsilon$ are isotropic tensors. Is their contraction also isotropic?

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  • $\begingroup$ Isn't their contraction 0? $\endgroup$ – harlem May 23 '18 at 16:30
  • $\begingroup$ Their contraction is 0. The possible way to show this is to check if the contraction is isotropic and check its rank. $\endgroup$ – Korf May 24 '18 at 9:04

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