Definition 2.12 Let $(X,J,\omega,\Omega)$ be an almost Calabi–Yau $m$-fold with metric $g$, and $N$ a real $m$-dimensional submanifold of $X$. We call $N$ a special Lagrangian submanifold, or SL $m$-fold for short, if $\omega|_{N}\equiv\mathop{\rm Im}\Omega|_{N}\equiv 0$. It easily follows that $\mathop{\rm Re}\Omega|_{N}$ is a nonvanishing $m$-form on $N$. Thus $N$ is orientable, with a unique orientation in which $\mathop{\rm Re}\Omega|_{N}$ is positive.