## THERMAL SCIENCE

International Scientific Journal

### SOME SPECIAL CURVES BELONGING TO MANNHEIM CURVES PAIR

**ABSTRACT**

In this paper, we investigate special Smarandache curves with regard to Sabban frame for Mannheim partner curve spherical indicatrix. We created Sabban frame belonging to this curves. It was explained Smarandache curves position vector is consisted by Sabban vectors belonging to this curves. Then, we calculated geodesic curvatures of this Smarandache curves. Found results were expressed depending on the Mannheim curve.

**KEYWORDS**

PAPER SUBMITTED: 2018-11-25

PAPER REVISED: 2018-12-26

PAPER ACCEPTED: 2019-01-12

PUBLISHED ONLINE: 2019-03-09

**THERMAL SCIENCE** YEAR

**2019**, VOLUME

**23**, ISSUE

**Supplement 1**, PAGES [S303 - S315]

- A. T. Ali, Special Smarandache curves in the Euclidian Space, International Journal of Mathematical Combinatorics 2 (2010), pp.30-36
- Ö. Bektaş, S. Yüce, Special Smarandache curves according to Darboux Frame in Euclidean 3-Space, Romanian Journal of Mathematics and Computer Sciencel, 3 (2013), 1, pp. 48-59
- A. Çalışkan S. Şenyurt, Smarandache curves in terms of Sabban frame of spherical indicatrix curves, Gen. Math. Notes 31 (2015), 2, pp.1-15
- A. Çalışkan , S.Şenyurt, N C -Smarandache curves of Mannheim curve couple according to Frenet Frame, International Journal of Mathematical Combinatorics 1(2015), pp. 1-13.
- M. Çetin, Y. Tuncer, M. K. Karacan, Smarandache curves according to Bishop frame in Euclidean 3-Space, Gen. Math. Notes, 20 (2014), pp. 50-66
- W. Fenchel, On the Differential Geometry of closed space curves, Bulletin of the American Mathematical Society, 57 (1951), pp.44-54
- H. H. Hacısalihoğlu, Differential Geometry, Academic Press Inc. Ankara, 1994.
- H. Liu, F. Wang, Mannheim partner curves in 3-space, Journal of Geometry, 88 (2008) ,(1-2), pp. 120-126
- K. Orbay, E. Kasap, On Mannheim partner curves in , International Journal of Physical Sciences, 4 (2009), 5, pp. 261-264
- M. Elzawy, Smarandache curves in Euclidian 4-space 4 E , Journal of the Eqyptian Mathematical Society (in press), DOI: dx.doi.org/10.1016/j.joems
- S. S enyurt, S. Sivas, An application of Smarandache curve, University of Ordu Journal of Science and Technology, 3 (2013), 1, pp.46-60
- S. Şenyurt, Y. Altun, C. Cevahir, Smarandache Curves According to Sabban Frame of Fixed Pole Curve Belonging to The Bertrand Curves Pair, AIP Conf. Proc. 1726 (2016) doi:10.1063/1.4945871.
- S. Şenyurt , Y. Altun , C. Cevahir, On The Darboux Vector Belonging to Involute Curve A Different View, Mathematical Sciences and Applications E-Notes, 4 (2016), 2, pp. 121-130.
- K. Taşköprü, M. Tosun, Smarandache Curves on 2 S , Boletim da Sociedade Paranaense de Matematica 3 Srie., 32 (2014), 1, pp. 51-59
- M. Turgut, S. Ylmaz, Smarandache curves in Minkowski space-time, International Journal of Mathematical Combinatorics, 3 (2008) pp.51-55