A mathematical interpretation on special tube surfaces in Galilean 3-space

Abstract

In this paper, we study the special tube surfaces generated by rectifying curves with respect to the Darboux frame in terms of the geodesic curvature, the normal curvature and the geodesic torsion in Galilean 3-space. During this study we establish some definite results of geodesics on specific tube surfaces with the help of Clairaut’s theorem in detail and we compute the Gaussian curvature and the mean curvature of the special tube surfaces with respect to the Darboux frame. After that, considering the geodesic conditions and the curvatures of the special tube surface, we give some theorems for the rectifying curves with $v$-parameter (and $w$-parameter) being a geodesic curve and an asymptotic curve, respectively.

Keywords

• Galilean space
• tube surface
• rectifying curves
• Darboux frame
• geodesic curve

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