International Scientific Journal

Thermal Science - Online First

online first only

On the Sabban frame belonging to involute-evolute curves

In this article, we investigate special Smarandache curves with regard to Sabban frame of involute curve. We created Sabban frame belonging to spherical indicatrix of involute curve. It was explained Smarandache curves position vector is consisted by Sabban vectors belonging to spherical indicatrix. Then, we calculated geodesic curvatures of this Smarandache curves. The results found for each curve was given depend on evolute curve. The example related to the subject were given and their figures were drawn with Mapple program.
PAPER REVISED: 2018-12-26
PAPER ACCEPTED: 2019-01-12
  1. Ali A.T., Special Smarandache Curves in the Euclidian Space, International Journal of Mathematical Combinatorics, 2 (2010), pp. 30-36
  2. Bektaş Ö. and Yüce S., Special Smarandache Curves According to Darboux Frame in Euclidean Space, Romanian Journal of Mathematics and Computer sciencel 3(2013), 1, pp. 48-59
  3. Bilici M. and Çalışkan, M., Some Characterizations For The Pair of Involute-evolute Curves is Euclidian 3 E , Bulletin of Pure and Applied Sciences, 21E(2002), 2, pp. 289-294
  4. Çalışkan A. and Şenyurt, S., Smarandache Curves In Terms of Sabban Frame of Spherical Indicatrix Curves, Gen. Math. Notes, 31(2015), 2, pp. 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), pp. 50-66
  6. Hacısalihoğlu H.H., Differantial Geometry(in Turkish), Academic Press Inc. Ankara, (1994)
  7. Senyurt S. and Sivas S., An Application of Smarandache Curve, University of Ordu Journal of Science and Technology, 3(2013), 1, pp. 46-60
  8. S enyurt S., Altun Y. and Cevahir C., 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.
  9. Şenyurt S., Altun Y. and Cevahir C., On The Darboux Vector Belonging To Involute Curve A Different View, Mathematical Sciences and Applications E-Notes, 4(2016), 2, pp. 121-130
  10. Turgut M. and Yılmaz S., Smarandache Curves in Minkowski space-time, International Journal of Mathematical Combinatorics, 3(2008), pp. 51-55
  11. Taşköprü K. and Tosun M., Smarandache Curves on 2 S , Boletim da Sociedade Paranaense de Matematica 3 Srie. 32(2014), 1, pp. 51-59