Characterizations of a helicoid and a catenoid

Abstract

In the present article, we consider a parametric surface generated by the Frenet frame of a curve, and study the minimality condition for the surface. As a result, we give characterizations of a helicoid and a catenoid. Finally we show some examples of minimal surfaces generated by a circle and a helix.

Keywords

• minimal surface
• catenoid
• helicoid
• marching-scale function

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