- Turkish Journal of Science
- Vol: 7 Issue: 2
- On the modified orthogonal frames of the non-unit speed curves in Euclidean Space E3
On the modified orthogonal frames of the non-unit speed curves in Euclidean Space E3
Authors : Sümeyye GÜR MAZLUM, Mehmet BEKTAŞ
Pages : 58-74
View : 13 | Download : 2
Publication Date : 2022-09-30
Article Type : Research
Abstract :In this study, the modified frames with both the non-zero curvature and the torsion of the non-unit speed curves in Euclidean space E3 are examined. The relationships between the derivative vectors of the modified frames and the Frenet vectors or the vectors of the modified frames of the curve are given. Besides, the Darboux vectors obtained from the modified orthogonal frames with both the curvature and torsion of the curve and the unit vectors in the direction of these Darboux vectors are investigated. Finally, all these results are shown on the example curves.Keywords : Modified orthogonal frame, Frenet frame, Darboux vector