Generalized Helices in the Euclidean 3-space Through Flow-frame

Anar C. Ö., YAYLI Y., Ekmekci N.

International Electronic Journal of Geometry, cilt.18, sa.2, ss.335-348, 2025 (ESCI) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 18 Sayı: 2
  • Basım Tarihi: 2025
  • Doi Numarası: 10.36890/iejg.1691504
  • Dergi Adı: International Electronic Journal of Geometry
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.335-348
  • Anahtar Kelimeler: 51M04, 53A04, Flow-frame, general helix, Lancret’s theorem, spherical indicatrix
  • Ankara Üniversitesi Adresli: Evet

Özet

A representation of time-dependent rotation of a usual Frenet flow is called flow-frame; the angle of rotation is exactly the current parameter. In this paper, we investigate three types of helices in the Euclidean 3-space through flow-frame and give their geometric description with flow-frame apparatus. Then, we introduce the spherical images of a curve by translating flow-frame vectors to the center of the unit sphere in the Euclidean 3-space R3. Besides, we examine the relationships between a generalized helix and its spherical images.