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: 5

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).