2015•Boletim da Sociedade Paranaense de MatemáticaOpen access

Surfaces family with common Smarandache asymptotic curve

Gülnur Şaffak Atalay, Emi̇n Kasap

Abstract

In this paper, we analyzed the problem of constructing 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 coefficients to satisfy both the asymptotic and isoparametric requirements. Finally, examples are given to show the family of surfaces with common Smarandache curve.

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Key concepts: Frenet–Serret formulas, Mathematics, Frame (networking), Euclidean space, Euclidean geometry, Space (punctuation), Family of curves, Surface (topology)