Let $(X,J,\omega,\Omega)$ be a Calabi–Yau $m$-fold, and $N$ a real $m$-dimensional submanifold of $X$. Then there is a unique orientation on $N$ making it into an SL $m$-fold if and only if $\omega|_{N}\equiv 0$ and $\mathop{\rm Im}\Omega|_{N}\equiv 0$.