Example 6.10 Define $u(x,y)={\textstyle\frac{1}{2}}y^{2}{\textstyle\mathop{\rm sech}}^{2}x-{\textstyle\frac{1}{2}}\cosh^{2}x$ and $v(x,y)=y\tanh x$. Then $u$ and $v$ satisfy (32). Equation (31) with $a=0$ defines an explicit nonsingular special Lagrangian 3-fold $N$ in $\mathbin{\mathbb{C}}^{3}$. It can be shown that $N$ is ruled, and arises from Harvey and Lawson’s ‘austere submanifold’ construction [9, §III.3.C] of SL $m$-folds in $\mathbin{\mathbb{C}}^{m}$, as the normal bundle of a catenoid in $\mathbin{\mathbb{R}}^{3}$.