Surfaces Family with Common Smarandache Geodesic Curve According to Bishop Frame in Euclidean Space

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Mathematical Sciences and Applications E-Notes
Volume:4 Issue:1
Surfaces Family with Common Smarandache Geodesic Curve According to Bishop Frame in Euclidean Space

Surfaces Family with Common Smarandache Geodesic Curve According to Bishop Frame in Euclidean Space

Authors : Gülnur Şaffak ATALAY, Emin KASAP

Pages : 164-174

Doi:10.36753/mathenot.421425

View : 32 | Download : 11

Publication Date : 2016-04-15

Article Type : Research Paper

Abstract :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 geodesic and isoparametric requirements. Finally, examples are given to show the family of surfaces with common Smarandache geodesic curve.
Keywords : Bishop frame

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