D- Smarandache Curves According to the Sabban Frame of the Spherical Indicatrix Curve

Year 2018, Volume: 9, 39 - 49, 28.12.2018

Süleyman Şenyurt

Abstract

In
this study, we first gave the Darboux vector according to the alternative
frame. Then we  formed a Sabban frame of
spherical indicatrix curve of D-  alternative vector defined by a differentiable
curve. Then the geodesic curvature of this vector is calculated according to
this frame. Finally we defined Smarandache curves generated by the  Sabban frame and give some characterizations
of them. 

Keywords

Sabban frame, alternative frame

References

• Ali, A. T., Special Smarandache Curves in the Euclidean Space, International Journal of Mathematical Combinatorics, 2(2010), 30–36.
• Bektaş, O., Yüce, S.,Special Smarandache Curves According to Darboux Frame in Euclidean 3- Space, Romanian Journal of Mathematicsand Computer Science, 3(1)(2013), 48–59.
• Do Carmo, M. P., Differential Geometry of Curves and Surfaces, Prentice Hall, Englewood Cliffs, NJ, 1976.
• Kaya, O., Önder M., New Partner Curves In The Euclidean 3-Space E3, International Journal of Geometry, 6(2)(2017), 41–50.
• Taşköprü, K., Tosun, M., Smarandache curves on S 2 , Boletim da Sociedade Paranaense de Matematica 3 Srie.,32 (1)(2014), 51–59.
• Turgut, M., Yılmaz S., Smarandache Curves in Minkowski Space-time, International J. Math. Combin., 3(2008), 51–55.