Generalized Helices in the Euclidean 3-space Through Flow-frame
International Electronic Journal of Geometry, cilt.18, sa.2, ss.335-348, 2025 (ESCI, Scopus, TRDizin)
- 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.