On the Construction of the Surface Family with a Common Involute Geodesic

Authors : Mustafa Bilici, Ergin Bayram

Pages : 162-168

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Publication Date : 2023-10-31

Article Type : Research Paper

Abstract :In this study, we produce a surface family possessing an involute of a given curve as a geodesic. We find necessary and sufficient conditions for the given curve such that its involute is a geodesic on any member of the surface family. Also, we present important results for ruled and developable surfaces. Finally, we present two examples to support our results.
Keywords : Involute curve, Geodesic curve, Frenet frame, Surface family