In the paper, three types of surfaces of revolution in the Galilean 3space are defined and studied. The construction of the well-known surface of revolution, defined as the trace of a planar curve rotated about an axis in the supporting plane of the curve, is given for the Galilean 3-space. Then we classify the surfaces of revolution with vanishing Gaussian curvature or vanishing mean curvature in the Galilean 3-space.

In this paper, we introduce a new version of tubular surfaces. We first define a new adapted frame along a space curve, and denote this the q-frame. We then reveal the relationship between the Frenet frame and the q-frame. We give a parametric representation of a directional tubular surface using the q-frame. Finally, some comparative examples are shown to confirm the effectiveness of the proposed method.Mathematics Subject Classification: 53A04, 53A05

In this paper, …rst of all, the de…nition of parallel surfaces in Galilean space is given. Then, the relationship between the curvatures of the parallel surfaces in Galilean space is determined. Moreover, the …rst and second fundamental forms of parallel surfaces are found in Galilean space. Consequently, we obtained Gauss curvature and mean curvature of parallel surface in terms of those curvatures of the base surface.

Abstract. In this paper, we investigate the parallel surfaces of the ruled surfaces in Galilean space. There are three types of ruled surfaces in Galilean space. We derive the necessary conditions for each type of the ruled surfaces of the parallel surfaces to be ruled. Consequently, we construct some examples.

In this paper, we introduce the tube surfaces in pseudo-Galilean 3-space. We classify the tube surfaces into two types according to the spine curve which generates the tube surface in pseudo-Galilean space. Moreover, we show that both types of tube surfaces are spacelike surfaces. Then, we begin to study the local geometry of the tube surfaces. We obtain the first and second fundamental forms of the tube surfaces. In addition, we investigate the Gauss and mean curvatures of the tube surfaces in pseudo-Galilean space.