I'm reading through Pauli's "Theory of Relativity", which has a discussion of tensors in the mathematical tools section of the book.(adsbygoogle = window.adsbygoogle || []).push({});

When introducing surface tensors, he states

"Such tensors can be obtained by considering two vectors [itex]x[/itex], [itex]y[/itex] which together span a two-dimensional parallelepiped. Its projections parallel to the axes on to the six two-dimensional coordinate planes, measure in units of the six parallelepipeds of the base vectors [itex]e_i[/itex], are given by

[tex]\xi^{ik} = x^iy^k - x^ky^i[/tex]

..."

First, since we're dealing with 4-dimensional spacetime, I'm asuuming the six two-dimensional coordinate planes would be the xy,xz,xt,yz,yt,and zt planes. Is this right?

More importantly, I don't understand what the [itex]\xi^{ik}[/itex] represent, can someone explain it to me in a geometrical sense?

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# Surface Tensors

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