Abstract
A canal surface is the envelope of a moving sphere with varying radius, defined by the trajectory C(t) (spine curve) of its center and a radius function r(t) and it is parametrized through Frenet frame of the spine curve C(t). If the radius function r(t) = r is a constant, then the canal surface is called a tube or tubular surface. In this work, we investigate tubular surface with Bishop frame in place of Frenet frame and afterwards give some characterizations about special curves lying on this surface
Highlights
Canal surfaces are useful for representing long thin objects, e.g., pipes, poles, ropes, 3D fonts or intestines of body
ZGT refers to the spine curve that has torsion-free and CGT refers to tube that has circular cross sections
He investigated the properties of GT and showed that parameter curves of a generalized tube are lines of curvature if and only if the spine curve has torsion free
Summary
Canal surfaces are useful for representing long thin objects, e.g., pipes, poles, ropes, 3D fonts or intestines of body. Xu et:al: [8] studied these conditions for canal surfaces and examined principle geometric properties of these surfaces like computing the area and Gaussian curvature. ZGT refers to the spine curve (the axis) that has torsion-free and CGT refers to tube that has circular cross sections. He investigated the properties of GT and showed that parameter curves of a generalized tube are lines of curvature if and only if the spine curve has torsion free (planar). Bishop frame; Canal surface; tubular surface; geodesic; asymptotic curve; line of curvature
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