Darboux Frame of Pancake Curve in Euclidean 3-Space

Emre Öztürk

doi:10.17776/csj.1444015

EN

Darboux Frame of Pancake Curve in Euclidean 3-Space

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.

Keywords

References

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Details

Primary Language

English

Subjects

Numerical Solution of Differential and Integral Equations

Journal Section

Research Article

Authors

Emre Öztürk ^*
0000-0001-6638-3233
Türkiye

Publication Date

September 30, 2024

Submission Date

February 28, 2024

Acceptance Date

September 12, 2024

Published in Issue

Year 2024 Volume: 45 Number: 3

DOI

https://doi.org/10.17776/csj.1444015

IZ

https://izlik.org/JA78UY64HK

Cite

RIS / Bibtex

APA

Öztürk, E. (2024). Darboux Frame of Pancake Curve in Euclidean 3-Space. Cumhuriyet Science Journal, 45(3), 571-577. https://doi.org/10.17776/csj.1444015