Can someone please explain to me why

whereAis a constant vector field.

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- Mar 28th 2013, 10:26 AMCuriosityCabinetQuestion involving Levi-Civita symbol
Can someone please explain to me why

where**A**is a constant vector field. - Mar 28th 2013, 03:11 PMRuunRe: Question involving Levi-Civita symbol
is a totally antisymmetric symbol and is symmetric under the exchange of and , because the partial derivatives commute.

In your particular case, as is constant, the derivatives are always zero. - Mar 28th 2013, 06:42 PMCuriosityCabinetRe: Question involving Levi-Civita symbol
OK thanks. So which part of the expression is zero? The part?

- Mar 29th 2013, 04:41 AMRuunRe: Question involving Levi-Civita symbol
Your expression actually means

This is

The definition of gives you a lot of zeros, in particular the only non zero are and . From this fact and that

you will have pairs of terms in your sum like

which cancel and gives you zero. - Apr 3rd 2013, 04:06 AMCuriosityCabinetRe: Question involving Levi-Civita symbol
Fantastic, problem solved.