Definition 5.3 Let $a\in\mathbin{\mathbb{R}}$ and $c\in\mathbin{\mathbb{C}}$. Define a special Lagrangian 3-fold $N^{\prime}_{a,c}$ in $\mathbin{\mathbb{C}}^{3}$ as in equations (21)–(23), but in each case replace the inequality $\mathop{\rm Re}\bigl(z_{1}z_{2}(z_{3}-c)\bigr)\geqslant 0$ by $\mathop{\rm Re}\bigl(z_{1}z_{2}(z_{3}-c)\bigr)\leqslant 0$. Then

• (i)

  $N^{\prime}_{0,c}$ is the translation of the special Lagrangian $T^{2}$-cone $L_{0}^{-}$ of (16) by $(0,0,c)$, and has one singular point at $(0,0,c)$.

• (ii)

  For $a>0$, $N^{\prime}_{a,c}$ is the translation of the nonsingular SL 3-fold $L_{1,a}^{-}$ of (17) by $(0,0,c)$, and is diffeomorphic to ${\mathcal{S}}^{1}\times\mathbin{\mathbb{R}}^{2}$.

• (iii)

  For $a<0$, $N^{\prime}_{a,c}$ is the translation of the nonsingular SL 3-fold $L_{2,-a}^{-}$ of (18) by $(0,0,c)$, and is diffeomorphic to ${\mathcal{S}}^{1}\times\mathbin{\mathbb{R}}^{2}$.