- Mathematical Sciences and Applications E-Notes
- Vol: 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 : 8 | Download : 4
Publication Date : 2016-04-15
Article Type : Research
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