Alkan, Akın; Hüseyin, Kocayi̇Ği̇T; Ağirman Aydin, Tuba

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. Cite this article as: Alkan A, Kocayiğit H, Ağırman Aydın T. New moving frames for the curves lying on a surface. Sigma J Eng Nat Sci 2024;42(4):1023−1029. Copyright 2021, Yıldız Technical University.

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Alkan, Akın; Kocayiğit, Hüseyin; Ağırman Aydın, Tuba

In this study, we consider Di-Darboux slant helices which are new surface curves on an oriented surface. We give some characterizations for such curves according to the Darboux frame, OD-frame, ND-frame, RD-frame, and obtain axes of the Di-Darboux slant helices. Moreover, the position vectors of the Di-Darboux slant helices are obtained.

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