Translation surfaces generating with some partner curve

Abstract

In this article, generating curves of translation surfaces are paired with some special curve pairs. With the results obtained from these pairings, the developable and minimal translation surfaces are characterized. In addition, the surface curvatures of the translation surface are obtained. For a better understanding of the results, examples are given and their drawings are made with the help of Mathematica.

Keywords

• Translation surface
• Bertrand partner curve
• Mannheim partner curve
• involute-evolute curves

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