Smarandache Curves of Mannheim Curve Couple According to Frenet Frame

Year 2017, Volume: 5 Issue: 1 , 122 - 136 , 30.04.2017

Süleyman Şenyurt Abdussamet Çalışkan

https://doi.org/10.36753/mathenot.421717

Cited By: 5

https://izlik.org/JA43WX73WD

Abstract

In this paper, when the Frenet vectors of the partner curve of Mannheim curve are taken as the position
vectors, the curvature and the torsion of Smarandache curves are calculated. These values are expressed
depending upon the Mannheim curve. Besides, we illustrate example of our main results. 

Keywords

Mannheim curve , Mannheim partner curve , Smarandache Curves , Frenet invariants

References

• [1] Ali, A. T., Special Smarandache Curves in the Euclidean Space, Intenational Journal of Mathematical Combinatorics, 2(2010), 30-36.
• [2] Bektaş, Ö. and Yüce, S., Special Smarandache Curves According to Dardoux Frame in Euclidean 3-Space, Romanian Journal of Mathematics and Computer science, 3(2013), no.1, 48-59.
• [3] Bayrak, N., Bekta¸s, Ö. and Yüce, S., Special Smarandache Curves in E_1^3, International Conference on Applied Analysis and Algebra, Yıldız Techinical University, 209, 2012.
• [4] Çalışkan, A. and Şenyurt, S. Smarandache Curves In terms of Sabban Frame of Spherical Indicatrix Curves, Gen. Math. Notes, 31(2015), no.2, 1-15.
• [5] Çetin, M., Tuncer, Y. and Karacan M.K., Smarandache Curves According to Bishop Frame in Euclidean 3-Space, Gen. Math. Notes, 20(2014), 50-66.
• [6] Hacısalihoğlu, H.H. Differential Geometry, ˙Inönü University, Malatya, Mat. no.7, 1983.
• [7] Liu, H. and Wang, F., Mannheim partner curves in 3-space, Journal of Geometry, 88(2008), no.1-2, 120-126(7).
• [8] Orbay, K. and Kasap, E., On Mannheim partner curves in, International Journal of Physical Sciences,4 (2009), no.5, 261-264.
• [9] Sabuncuoğlu, A. Differential Geometry, Nobel Publications, Ankara, 2006.
• [10] Turgut, M. and Yılmaz, S., Smarandache Curves in Minkowski space-time, International Journal of Mathematical Combinatorics, 3(2008), 51-55.
• [11] Wang, F.,and Liu, H., Mannheim Partner Curves in 3-Space, Proceedings of The Eleventh International Workshop on Diff. Geom., 11(2007), 25-31.