Assume that

• i)

  $Y=T^{n}\times\mathbb{R}^{n}$, $g=h+h_{E}$, and the natural projection $f:Y\longrightarrow\mathbb{R}^{n}$ is a special lagrangian fibration of $(Y,\omega,\Omega)$, where $T^{n}=\mathbb{R}^{n}/\Lambda$ is a torus, $\Lambda$ is a lattice in $\mathbb{R}^{n}$, $h_{E}$ is the standard Euclidean metric on $\mathbb{R}^{n}$, and $h$ is the standard flat metric induced by $h_{E}$.

• ii)

  We assume that there are parallel 1-forms $dx_{1},\cdots,dx_{n}$ on $(T^{n},h)$, which are pointwise linear independent, and coordinates $y_{1},\cdots,y_{n}$ on $\mathbb{R}^{n}$ such that

  $$g=h+h_{E}=\sum(dx_{j}^{2}+dy_{j}^{2}),\ \ \ \omega=\sum dx_{j}\wedge dy_{j},\ \ \ \Omega=\bigwedge_{j=1}^{n}(dx_{j}+\sqrt{-1}dy_{j}).$$

• iii)

  There is a family of Calabi-Yau structures $(\omega_{k},g_{k},J_{k},\Omega_{k})$ converging to $(\omega,g,J,\Omega)$ in the $C^{\infty}$-sense on $Y_{2r}=T^{n}\times B_{h_{E}}(0,2r)$ for a $r\gg 1$, where $B_{h_{E}}(0,2r)=\{y\in\mathbb{R}^{n}|\|y\|_{h_{E}}<2r\}$. Moreover, $\omega_{k}\in[\omega]\in H^{2}(Y_{2r},\mathbb{R})$.

• vi)

  There is a finite group $\Gamma$ acting on $Y_{2r}$ preserving $\omega_{k},g_{k},\Omega_{k},\omega,g,\Omega$, and $T^{n}\times\{0\}$ is a invariant set. The $\Gamma$-action is a product action on $T^{n}\times B_{h_{E}}(0,2r)$. The natural projection $f:Y\longrightarrow\mathbb{R}^{n}$ is $\Gamma$-equivariant.