Some new associated curves of a Frenet curve in E-3 and E-4

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Macit N., Düldül M.

TURKISH JOURNAL OF MATHEMATICS, cilt.38, ss.1023-1037, 2014 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 38
  • Basım Tarihi: 2014
  • Doi Numarası: 10.3906/mat-1401-85
  • Dergi Adı: TURKISH JOURNAL OF MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.1023-1037
  • Anahtar Kelimeler: Frenet curve, associated curve, integral curve, general helices, slant helices, rectifying curve, POSITION VECTOR, SLANT HELIX
  • Yıldız Teknik Üniversitesi Adresli: Evet

Özet

In this paper, firstly, we define a W-direction curve and W-rectifying curve of a Frenet curve in 3-dimensional Euclidean space E-3 by using the unit Darboux vector field W of the Frenet curve and give some characterizations together with the relationships between the curvatures of each associated curve. We also introduce a V-direction curve, which is associated with a curve lying on an oriented surface in E-3. Later, some new associated curves of a Frenet curve are defined in E-4.