Dual to Tensor: Meaning & -1/6 Explained

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In my lecture note about tensor it states:
As element of integration over the hypersurface it is more convenient to use the 4-vector dS^i , dual to the tensor dS^ikl:

dS^i = -1/6 e^iklmdS_klm ,dS_klm = e_iklmdS^i

What is the meaning of dual?
How the -1/6 comes from?

yukyuk
 
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