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    Stuck on a question - seems like it must just be some manipulation but I can't seem to get it.

    A tensor of rank 4 satisfies Tjikl = -Tijkl = Tijlk and Tijij=0

    Show that Tijkl = -EijpEklqTrqrp

    Where those 'E's are Cevi Levita symbols.

    I've figured that the first two indices must be different than each other to give a non-zero value, and the same with the last two indices.

    Help would be much appreciated. Thanks.

    Does anyone have a solution?

    Will skip out the details but here's an outline: define S_{pq}=\varepsilon_{ijp} \varepsilon_{klq}T_{ijkl}

    Then \varepsilon_{abp}\varepsilon_{cd  q} S_{pq}=\varepsilon_{abp} \varepsilon_{cdq} \varepsilon_{ijp} \varepsilon_{klq}T_{ijkl} \Rightarrow \varepsilon_{abp}\varepsilon_{cd  q}S_{pq}=4T_{abcd}. Contracting a,c we get T_{abad}=-\frac{1}{4}S_{bd}

    Substitute back into the equality that preceded the contraction and you have the desired expression (with relabelling)
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