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DOI:http://dx.doi.org/10.26855/ jamc.2018.04.005

Surfaces family with a common Mannheim geodesic curve

Date: April 15,2018 |Hits: 1040 Download PDF How to cite this paper
Gülnur ŞAFFAK ATALAY1,*
1Education Faculty, Department of Mathematics and Science Education, Ondokuz Mayis University, Samsun, Turkey

*Corresponding author: Gülnur ŞAFFAK ATALAY
Email: gulnur.saffak@omu.edu.tr

Abstract

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.

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How to cite this paper

Surfaces family with a common Mannheim geodesic curve

How to cite this paper: ATALAY, G.Ş. (2018) Surfaces family with a common Mannheim geodesic curve. Journal of Applied Mathematics and Computation, 2(4), 155-165.
http://dx.doi.org/10.26855/ jamc.2018.04.005
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