Helicoidal Surfaces in Galilean Space With Density

In this paper, we construct helicoidal surfaces in the three dimensional Galilean space G³. The First and the Second Fundamental Forms for such surfaces will be obtained. Also, mean and Gaussian curvature given by smooth functions will be derived. We consider the Galilean 3-space with a linear density e^{φ} and construct a weighted helicoidal surfaces in G³ by solving a second order non-linear differential equation. Moreover, we discuss the problem of finding explicit parameterization for the helicoidal surfaces in G³.