General Mathematics

   

Surfaces Family with a Common Mannheim Geodesic Curve

Authors: Gülnur ŞAFFAK ATALAY

In this paper, we analyzed surfaces family possessing a Mannheim partner curve of a given curve as a geodesic. Using the Frenet frame of the curve in Euclidean 3-space, we express the family of surfaces as a linear combination of the components of this frame and derive the necessary and sufficient conditions for coefficients to satisfy both the geodesic and isoparametric requirements. The extension to ruled surfaces is also outlined. Finally, examples are given to show the family of surfaces with common Mannheim geodesic curve.

Comments: 11 Pages.

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Submission history

[v1] 2018-08-22 04:37:27

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