We consider the case when either $l=0$, or $k=0$. In both situations the discriminant locus is empty and the total space $M$ is just the product of the domain $R$ and the torus $T^{n}$. We can use any solution of the classical real Monge-Ampère equation in $R$ and extend it to a Gibbons-Hawking solution on $M$ by setting higher Fourier modes to zero. In the obvious complex structure this will give a Ricci-flat metric on $M=\bar{M}$ (cf. [Hit97], [Leu00], [LYZ01]).