Self-dual frame in complex Euclidean coordinates
= Self-dual frame in complex Euclidean coordinates
{title2=$\Lambda^2_+$}
For $w=x^1+ix^2$, $z=x^3+ix^4$ and the standard oriented <Euclidean metric>, the real and imaginary parts of $dw\wedge dz$, together with $i(dw\wedge d\bar w+dz\wedge d\bar z)$, span the <self-dual two-forms>. The printed complex four-form $dw\wedge dz\wedge d\bar w\wedge d\bar z$ is four times the metric <volume form> and gives the same <orientation>.