New moving frames for the curves lying on a surface
1Gördes Vocational School, Manisa Celal Bayar University, Manisa, 45750,Türkiye
2Department of Mathematics, Manisa Celal Bayar University, Manisa, 45140, Türkiye
3Faculty of Education, Bayburt University, Bayburt, 69000, Türkiye
2Department of Mathematics, Manisa Celal Bayar University, Manisa, 45140, Türkiye
3Faculty of Education, Bayburt University, Bayburt, 69000, Türkiye
Sigma J Eng Nat Sci 2024; 42(4): 1023-1029 DOI: 10.14744/sigma.2023.00049
Abstract
In this article, three new orthogonal frames are defined for the curves lying on a surface. These moving frames, obtained based on the Darboux frame, are called “Osculator Darboux Frame”, “Normal Darboux Frame” and “Rectifying Darboux Frame”, respectively. Also, the Osculator Darboux Frame components and curvatures are calculated for a presented example.
Keywords: Darboux Frame; Moving Frame; Normal Darboux Vector; Osculator Darboux Vector; Rectifying Darboux Vector
