Surfaces family with common smarandache asymptotic curve according to bishop frame in euclidean 3-space

Surfaces family with common smarandache asymptotic curve according to bishop frame in euclidean 3-space

In this paper, we analyzed the problem of consructing a family of surfaces from a given some special Smarandache curves in  Euclidean 3-space. Using the Bishop 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 deri...

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Main Author: Gulnur Saffak Atalay
Format: Article
Language:English
Published: Sociedade Brasileira de Matemática 2016-04-01
Series:Boletim da Sociedade Paranaense de Matemática
Subjects:
Asymptotic curve, Smarandache curves, Bishop Frame, Surface family.
Online Access:http://periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/25480
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spelling doaj-85d7436b80b8423fb0bb15f6fb6ae9622020-11-25T00:36:26ZengSociedade Brasileira de MatemáticaBoletim da Sociedade Paranaense de Matemática0037-87122175-11882016-04-0134118720210.5269/bspm.v34i1.2548012346Surfaces family with common smarandache asymptotic curve according to bishop frame in euclidean 3-spaceGulnur Saffak Atalay0Ondokuz Mayıs University Arts and Science Faculty Department of MathematicsIn this paper, we analyzed the problem of consructing a family of surfaces from a given some special Smarandache curves in  Euclidean 3-space. Using the Bishop 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 coefficents to satisfy both the asymptotic and isoparametric requirements. Finally, examples are given to show the family of surfaces with common Smarandache asymptotic curve.http://periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/25480Asymptotic curve, Smarandache curves, Bishop Frame, Surface family.
collection DOAJ
language English
format Article
sources DOAJ
author Gulnur Saffak Atalay
spellingShingle Gulnur Saffak Atalay
Surfaces family with common smarandache asymptotic curve according to bishop frame in euclidean 3-space
Boletim da Sociedade Paranaense de Matemática
Asymptotic curve, Smarandache curves, Bishop Frame, Surface family.
author_facet Gulnur Saffak Atalay
author_sort Gulnur Saffak Atalay
title Surfaces family with common smarandache asymptotic curve according to bishop frame in euclidean 3-space
title_short Surfaces family with common smarandache asymptotic curve according to bishop frame in euclidean 3-space
title_full Surfaces family with common smarandache asymptotic curve according to bishop frame in euclidean 3-space
title_fullStr Surfaces family with common smarandache asymptotic curve according to bishop frame in euclidean 3-space
title_full_unstemmed Surfaces family with common smarandache asymptotic curve according to bishop frame in euclidean 3-space
title_sort surfaces family with common smarandache asymptotic curve according to bishop frame in euclidean 3-space
publisher Sociedade Brasileira de Matemática
series Boletim da Sociedade Paranaense de Matemática
issn 0037-8712
2175-1188
publishDate 2016-04-01
description In this paper, we analyzed the problem of consructing a family of surfaces from a given some special Smarandache curves in  Euclidean 3-space. Using the Bishop 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 coefficents to satisfy both the asymptotic and isoparametric requirements. Finally, examples are given to show the family of surfaces with common Smarandache asymptotic curve.
topic Asymptotic curve, Smarandache curves, Bishop Frame, Surface family.
url http://periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/25480
work_keys_str_mv AT gulnursaffakatalay surfacesfamilywithcommonsmarandacheasymptoticcurveaccordingtobishopframeineuclidean3space
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