Let $(X,J,\omega,\Omega)$ be a Calabi–Yau $m$-fold, and $N$ a compact $m$-dimensional submanifold of $X$. Then there exists a special Lagrangian submanifold $N^{\prime}$ of $X$ isotopic to $N$ in $X$ only if $[\omega|_{N}]=0$ in $H^{2}(N,\mathbin{\mathbb{R}})$ and $[\mathop{\rm Im}\Omega|_{N}]=0$ in $H^{m}(N,\mathbin{\mathbb{R}})$.