Affiliation:
1. Sakarya Üniversitesi Matematik Bölümü, Sakarya.Türkiye
2. SAKARYA UNIVERSITY
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.
Publisher
Mathematical Sciences and Applications E-Notes
Reference18 articles.
1. [1] Ali, A. T.: Special Smarandache curves in the Euclidean space. International Journal of Mathematical Combinatorics. 2, 30-36 (2010).
2. [2] Okuyucu, O. Z., Değirmen, Ç, Yıldız, Ö. G.: Smarandache curves in three dimensional Lie groups. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics. 68(1), 1175-1185 (2019).
3. [3] Taşköprü, K., Tosun, M.: Smarandache curves on S2. Boletim da Sociedade Paranaense de Matematica. 32(1), 51-59 (2014).
4. [4] Gürses, B. N., Bektaş, Ö, Yüce, S.: Special Smarandache curves in R^3_1. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics. 65(2), 143-160 (2016).
5. [5] Turgut, M., Yılmaz, S.: Smarandache curves in Minkowski space-time. International Journal of Mathematical
Combinatorics. 3, 51-55 (2008).