SMARANDACHE CURVES ACCORDING TO ALTERNATIVE FRAME IN E^3

Year 2021, Volume: 4 Issue: 2, 140 - 156, 31.07.2021

Şenay Alıç , Beyhan Yılmaz

https://doi.org/10.33773/jum.956862

Cited By: 4

Abstract

In this study, we focus on Smarandache curves which is a special class of curves. These curves have previously been studied by many authors in different spaces. We will
re-characterize these curves with the help of an alternative frame different from Frenet frame. Also, we will obtain frame elements, curvature and torsion of these curves.

Keywords

Euclidean Space, Frenet frame, Smarandache Curves, Alternative frame

References

• H.H. Hacısalihoglu, The Motion Geometry and Quatenions Theory (in Turkish), Gazi University Publications, (1983).
• M. Turgut and S. Yılmaz, Smarandache Curves in Minkowski Space-time, International Journal of Mathematical Combinatorics, 3, 51-55, (2008).
• A. T. Ali, Special Smarandache Curves in the Euclidean Space, International Journal of Mathematical Combinatorics, 2, 30-36, (2010).
• S. Şenyurt and S. Sivas, An Application of Smarandache Curve, Ordu Univ. J. Sci. Tech. 3(1), 46-60, (2013).
• K. Taşköprü and M. Tosun, Smarandache Curves on S2, Boletim da Sociedade paranaense de Matematica 3 serie, 32(1):51-59, (2014).
• M. Çetin, Y. Tuncer, M.K. Karacan, Smarandache curves according to Bishop frame in Euclidean 3-space. General Mathematics Notes, 20:50-66 (2014).
• N. Bayrak, Ö. Bektaş, S. Yüce, Special Smarandache curves in E3 1, Communications Faculty of Sciences University of Ankara Series A1:Mathematics and Statistics, 65(2): 143-160, (2016).
• Ü. Çelik, Smarandache Curves of Bertrand Curve Pair According to Frenet Frame, Master’s Thesis, University of Ordu, (2016).
• B. Uzunoğlu, I. Gök and Y. Yaylı, A New Approach on Curves of Constant Precession, Appl. Math. Comput. 275, 317-323, (2016).