On Characterization of Smarandache Curves Constructed by Modified Orthogonal Frame

Authors : Kemal Eren, Soley Ersoy

Pages : 101-112

Doi:10.36753/mathenot.1409228

View : 189 | Download : 220

Publication Date : 2024-09-24

Article Type : Research

Abstract :In this study, we investigate Smarandache curves constructed by a space curve with a modified orthogonal frame. Firstly, the relations between the Frenet frame and the modified orthogonal frame are summarized. Later, the Smarandache curves based on the modified orthogonal frame are obtained. Finally, the tangent, normal, binormal vectors and the curvatures of the Smarandache curves are determined. A special curve known as the Gerono lemniscate curve whose curvature is not differentiable, the principal normal and binormal vectors are discontinuous at zero point is considered as an example, and the Smarandache curves of this curve are obtained by the aid of its modified orthogonal frame, and their graphics are given.
Keywords : Gerono lemniscate curve, Modified orthogonal frame, Smarandache curves