math. sci. appl. e-notes Mathematical Sciences and Applications E-Notes 2147-6268 Murat TOSUN 10.36753/mathenot.421717 Smarandache Curves of Mannheim Curve Couple According to Frenet Frame Şenyurt Süleyman Çalışkan Abdussamet 04 30 2017 5 1 122 136 10 11 2016 Copyright © 2013, Mathematical Sciences and Applications E-Notes 2013 Mathematical Sciences and Applications E-Notes

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

 Mannheim curve Mannheim partner curve Smarandache Curves Frenet invariants [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.