Surfaces family with common Smarandache asymptotic curve-Reference-Cited by-同舟云学术

Surfaces family with common Smarandache asymptotic curve

Published:2016-01-01 Issue:1 Volume:34 Page:9-20
ISSN:2175-1188
Container-title:Boletim da Sociedade Paranaense de Matemática
language:en
Short-container-title:bspm

Author:

Saffak Atalay Gulnur¹,Kasap Emin¹

Affiliation:

1. Ondokuz Mayıs University

Abstract

In this paper, we analyzed the problem of constructing a family of surfaces from a given some special Smarandache curves in Euclidean 3-space. 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. Finally, examples are given to show the family of surfaces with common Smarandache curve.

Publisher

Sociedade Paranaense de Matematica

Subject

General Mathematics

Reference16 articles.

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4. 4. M. Turgut, and S. Yilmaz, Smarandache Curves in Minkowski Space-time, International Journal of Mathematical Combinatorics, Vol.3, pp.51-55.

5. 5. Ali, A.T. , Special Smarandache Curves in Euclidean Space, International Journal of Mathematical Combinatorics, Vol.2, pp.30-36, 2010.

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