Darboux Frame of Pancake Curve in Euclidean 3-Space
Cumhuriyet Science Journal, cilt.45, sa.3, ss.571-577, 2024 (TRDizin)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 45 Sayı: 3
- Basım Tarihi: 2024
- Doi Numarası: 10.17776/csj.1444015
- Dergi Adı: Cumhuriyet Science Journal
- Derginin Tarandığı İndeksler: TR DİZİN (ULAKBİM)
- Sayfa Sayıları: ss.571-577
- Hatay Mustafa Kemal Üniversitesi Adresli: Evet
Özet
In this paper, we focus on a rare curve, “The pancake curve” which was named by Robert Ferréol. We investigate the Darboux frame of the curve, and we calculate the curvatures: geodesic curvature, normal curvature, and geodesic torsion. We discuss two cases, for instance, pancake curve as an intersection of Plücker’s conoid and unit cylinder, and the intersection of a hyperbolic paraboloid and unit cylinder. Moreover, we give the relations between the Frenet and Darboux curvatures. Finally, we give some examples related to the Frenet and Darboux frame and curvatures.