New moving frames for the curves lying on a surface

Year 2024, Volume: 42 Issue: 4, 1023 - 1029, 01.08.2024

Akın Alkan , Hüseyin Kocayiğit Tuba Ağırman Aydın

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

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