TY  - JOUR
T1  - New moving frames for the curves lying on a surface
AU  - Alkan, Akın
AU  - Kocayiğit, Hüseyin
AU  - Ağırman Aydın, Tuba
PY  - 2024
DA  - August
JF  - Sigma Journal of Engineering and Natural Sciences
JO  - SIGMA
PB  - Yildiz Technical University
WT  - DergiPark
SN  - 1304-7191
SP  - 1023
EP  - 1029
VL  - 42
IS  - 4
LA  - en
AB  - 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.
KW  - Darboux Frame
KW  - Moving Frame
KW  - Normal Darboux Vector
KW  - Osculator Darboux Vector
KW  - Rectifying Darboux Vector
CR  - REFERENCES
CR  - [1]	Liu H, Wang F. Mannheim partner curves in 3-space. J Geom 2008;88:120126.
CR  - [2]	J Burke. Bertrand curves associated with a pair of curves. Math Mag 1960;34:60–62.
CR  - [3]	Gluck H. Higher curvatures of curves in euclidean space. Am Math Mon 1966;73:699704.
CR  - [4]	Sabuncuoğlu A, Hacısalihoğlu HH. On higher curvatures of a curve. Commun Fac Sci Univ Ankara Ser A1 Math Stat 1975;24:3346.
CR  - [5]	Özdamar E, Hacısalihoğlu HH. A Characterization of Inclined Curves in Euclidean n-Space, Communications, Commun Fac Sci Univ Ankara Ser A1 Math 1975;24:1523.
CR  - [6]	Özdamar E, Hacısalihoğlu HH. Characterizations of spherical curves in euclidean n-space. Commun Fac Sci Univ Ankara Ser A1 Math Stat 1974:109125.
CR  - [7]	Izumiya S, Takeuchi N. New special curves and developable surfaces. Turk J Math 2004;28:153163.
CR  - [8]	Kula L, Ekmekçi N, Yaylı Y, İlarslan K. Characterizations of slant helices in euclidean 3-space. Turk J Math 2010;34:261273.
CR  - [9]	Öztürk U, Hacısalihoğlu HH. Helices on a surface in Euclidean 3-space.Celal Bayar Univ J Sci 2017;13:113123.
CR  - [10]	Zıplar E, Şenol A, Yaylı Y. On darboux helices in euclidean 3-space. Glob J Science Front Res Math Decis Sci 2012;12:7380.
CR  - [11]	Uzunoğlu B, Gök ·I, Yayli Y. A new approach on curves of constant precession. Appl Math Comput 2016;275:317323.
CR  - [12]	Yılmaz S, Turgut M. 2010. A New version of bishop frame and application to spherical images. J Mathe Anal Appl 2010;371:764776.
CR  - [13]	Bishop LR. There is more than one way to frame a curve. Am Math Mon 1975;82:246251.
CR  - [14]	Düldül M, Uyar Düldül B. Characterizations of helices by using their Darboux vectors. Sigma J Eng Nat Sci 2020;38:12991306.
CR  - [15]	Hananoi S, Ito N, Izumiya S. Spherical Darboux images of curves on surfaces. Beitr Algebra Geom 2015;56:575585.
CR  - [16]	Macit N, Düldül M. Relatively normal-slant helices lying on a surface and their characterizations. Hacettepe J Math Stat 2017;46:397408.
CR  - [17]	Doğan F, Yaylı Y. On isophote curves and their characterizations. Turk J Math
2015;39:650664.
CR  - [18]	Önder M. Helices associated to helical curves, relatively normal-slant helices and         isophote curves. Available at: https://arxiv.org/abs/2201.09684. Accessed on Jul 2, 2024.
CR  - [19]	O'Neill B. Elementary differential geometry. Cambridge: Academic Press; 1966.
UR  - https://dergipark.org.tr/en/pub/sigma/issue//1526969
L1  - https://dergipark.org.tr/en/download/article-file/4117086
ER  -