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

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

References

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