Surfaces Family With Common Smarandache Asymptotic Curve
BOLETIM SOCIEDADE PARANAENSE DE MATEMATICA, vol.34, no.1, pp.9-20, 2016 (ESCI, Scopus)
- Publication Type: Article / Article
- Volume: 34 Issue: 1
- Publication Date: 2016
- Doi Number: 10.5269/bspm.v34i1.24392
- Journal Name: BOLETIM SOCIEDADE PARANAENSE DE MATEMATICA
- Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus
- Page Numbers: pp.9-20
- Open Archive Collection: AVESIS Open Access Collection
- Ondokuz Mayıs University Affiliated: Yes
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 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 coefficents to satisfy both the asymptotic and isoparametric requirements. Finally, examples are given to show the family of surfaces with common Smarandache curve.