Helicoidal Surfaces in Galilean Space With Density

Abstract

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 eϕ 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. M.S.C.2010: 53A35, 51A05