On dual surfaces in Galilean 3-space

In the present paper, we describe dual translation surfaces in the Galilean 3-space having the constant Gaussian and mean curvatures as well as Weingarten and linear Weingarten dual translation surfaces. We also study dual translation surfaces in ${\mathbb{G}}_3$ under the condition ${\mathrm{\Delta }}^{II}r={\lambda }_i{r}_i$, where ${\lambda }_i\in R$ and ${\mathrm{\Delta }}^{II}$ denotes the Laplacian operator respect to the second fundamental form.