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

Year 2023, Volume: 11 Issue: 2, 162 - 168, 31.10.2023

Mustafa Bilici , Ergin Bayram

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

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