Surfaces of Revolution with Vanishing Curvature in Galilean 3-Space

Abstract

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.

Helicoidal Surfaces in Galilean Space With Density

“…In this part, we give a brief review of curves and surfaces in the Galilean space G 3 . For more details, one can see [12,[14][15][16]18].…”

Weighted Minimal and Weighted Flat Surfaces of Revolution in Galilean 3-Space with Density

“…Here we always assume that the surface is admissible, that is, its tangent space is nowhere an Euclidean plane (for detail, see [3]). …”

“…In [3], the authors have constructed the surfaces of revolution in Galilean 3-space analogously to how that is done in Euclidean 3-space and they have obtained 3 types of surfaces of revolution in G 3 .…”

“…where the profile curve α lies in the isotropic xy-plane and it is parametrized by α(u) = (f (u), g(u), 0) [3].…”

“…The catenoid which is obtained by rotating a catenary is the most famous minimal surface of revolution. For another characterizations of surfaces of revolution, we refer to [1], [3], [5], [6], [7], [8], [11], [12], [14] and etc.…”