In this article Hasimoto surfaces in Galilean space $$G_{3}$$G 3 will be considered, Gauss curvature (K) and Mean curvature (H) of Hasimoto surfaces $$\chi =\chi (s,t)$$χ = χ ( s , t ) will be investigated, some characterization of s-curves and t-curves of Hasimoto surfaces in Galilean space $$G_{3}$$G 3 will be introduced. Example of Hasimoto surfaces will be illustrated.

In this paper, we study Smarandache curves in the 4-dimensional Galilean space G4. We obtain Frenet-Serret invariants for the Smarandache curve in G4. The first, second and third curvature of Smarandache curve are calculated. These values depending upon the first, second and third curvature of the given curve. Examples will be illustrated

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. M.S.C.2010: 53A35, 51A05

In this article, we introduce the notion of a spatial quaternionic Bertrand curves in G3 and give some characterizations of such curves. Furthermore, we introduce spatial quaternionic (1,3)-Bertrand curves in G4.