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\section{Abstract}  By introducing a new form of metric tensor the same derivation for the electromanetic tensor F $F_{\mu \nu}$  from potentials A $A_{\mu}$  leads to the dual space (Hodge Dual) of the regular F $F_{\mu \nu}$  tensor. There are additional components in i,j,k dirns. the $i,j,k$ planes, however if after the derivation only the real part is considered a physically consistent electromagnetic theory is recovered with a relabelling of $\vec{E}$ fields to $\vec{B}$ fields and vice versa.