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

Year 2016, , 164 - 174, 15.04.2016

Gülnur Şaffak Atalay , Emin Kasap

https://doi.org/10.36753/mathenot.421425

Cited By: 8

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

References

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