Darboux Frame of Pancake Curve in Euclidean 3-Space
Cumhuriyet Science Journal, vol.45, no.3, pp.571-577, 2024 (TRDizin)
- Publication Type: Article / Article
- Volume: 45 Issue: 3
- Publication Date: 2024
- Doi Number: 10.17776/csj.1444015
- Journal Name: Cumhuriyet Science Journal
- Journal Indexes: TR DİZİN (ULAKBİM)
- Page Numbers: pp.571-577
- Hatay Mustafa Kemal University Affiliated: Yes
Abstract
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.