Weingarten tube-like surfaces in Euclidean 3-space

Abstract

In this paper, we study a special kind of tube surfaces, so-called tubelike
surface in 3-dimensional Euclidean space E3. It is generated by sweeping a
space curve along another central space curve. This study investigates a tubelike
surface satisfying some equations in terms of the Gaussian curvature, the
mean curvature, the second Gaussian curvature and the second mean curvature.
Furthermore, some important theorems are obtained. Finally, an example of tubelike surface is used to demonstrate our theoretical results and graphed.