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DOI:http://dx.doi.org/10.26855/ jamc.2018.04.004

Surfaces family with a common Mannheim asymptotic curve

Date: April 15,2018 |Hits: 1072 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 of a given curve as a asymptotic. 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 asymptotic and isoparametric requirements. The extension to ruled surfaces is also outlined. Finally, examples are given to show the family of surfaces with common Mannheim asymptotic curve.

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How to cite this paper

Surfaces family with a common Mannheim asymptotic curve

How to cite this paper: ATALAY, G.Ş. (2018) Surfaces family with a common Mannheim asymptotic curve. Journal of Applied Mathematics and Computation, 2(4), 143-154.
http://dx.doi.org/10.26855/ jamc.2018.04.004
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