Surfaces Family With Common Smarandache Asymptotic Curve According To Bishop Frame In Euclidean Space

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Şaffak Atalay G., Kasap E.

BOLETIM SOCIEDADE PARANAENSE DE MATEMATICA, cilt.34, sa.1, 2016 (ESCI) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 34 Sayı: 1
  • Basım Tarihi: 2016
  • Doi Numarası: 10.5269/bspm.v34i1.25480
  • Dergi Adı: BOLETIM SOCIEDADE PARANAENSE DE MATEMATICA
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus
  • Anahtar Kelimeler: Smarandache Asymptotic Curve, Bishop Frame, ALTERNATIVE MOVING FRAME, PARAMETRIC REPRESENTATION, PENCIL
  • Ondokuz Mayıs Üniversitesi Adresli: Evet

Özet

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 asymptotic and isoparametric requirements. Finally, examples are given to show the family of surfaces with common Smarandache asymptotic curve.