Smarandache Curves of Spatial Quaternionic Bertrand Curve According to Frenet Frame

Abstract

In this study, Frenet vectors of spatial quaternionic Bertrand curve pair were taken as the position vector. The obtained Smarandache curves from position vector were defined. Frenet vectors, the curvature and torsion of this curve were calculated. This later the Frenet apparatus were expressed in terms of Frenet apparatus of the spatial quaternionic Bertrand curve pair. Example related to the subject was found and their drawings were done with Maple program.

Keywords

• spatial quaternion

References

1. Ali AT. Special Smarandache Curves in the Euclidean Space, International Journal of Mathematical Combinatorics. 2, 2010, 30 –36.
2. Bharathi K, Nagaraj M. Quaternion Valued Function Of A Real Variable Serret-Frenet Formula, Indian Journal of Pure and Applied Mathematics. 18(6), 1987, 507-511.
3. Demir S, Oztas¸ K. Serret-Frenet Formulas With Real Quaternions, Süleyman Demirel University Journal of Natural and Applied ¨ Sciences. 9(3), 2005, 1 – 7.
4. Erişir T, Gungör MA. Some Characterizations of Quaternionic Rectifying Curves in the Semi-Euclidean Space ¨ E^42 . Honam Mathematical J. 36(1), 2014, 67 – 83.
5. Hacısalihoglu HH. The Motion Geometry and Quatenions Theory (in Turkish), Gazi University Publications. 1983. ˘
6. Karadag M, Sivridağ AI. Characterizations For Ouaternionic Trendlines, University of Erciyes. Journal of Institute of Sciences and ˘Technology of Erciyes University, 13, 1997, 23-36.
7. Keilioglu O, İlarslan K. Quaternionic Bertrand Curves In Euclidean 4-Space. Bulletin of Mathematical Analysis and Applications. 5(3), 2013, 27 – 38.
8. Parlatıcı H. Quaternionic Smarandache Curves. Master Thesis. University of Sakarya, 2013.

9. Şenyurt S, ÇalıŞkan AS. An Application According to Spatial Quaternionic Smarandache Curve. Applied Mathematical Sciences. 9(5), 2015, 219 – 228.
10. Şenyurt S, Sivas S. An Application of Smarandache Curve. Ordu Univ. J. Sci. Tech. 3(1), (2013, 46 – 60.
11. Şenyurt S, Altun Y, Cevahir C. Smarandache Curves for Spherical Indicatrix of the Bertrand Curves Pair. Boletim da Sociedade Paranaense de Matemtica. 38(2), 2020, 27 – 39.
12. Şenyurt S, Cevahir C, Altun Y. On Spatial Quaternionic Involute Curve A New View. Adv. Appl. Clifford Algebras. 27(2), 2017, 1815 – 1824.
13. Şenyurt S, Cevahir C, Altun Y. On the Smarandache Curves of Spatial Quaternionic Involute Curve. Proceedings of the National Academy of Sciences. India Section A: Physical Sciences. 2019. ( accepted https://doi.org/10.1007/s40010-019-00640-5).
14. Tuna A, Çöken AC. On The Quaternionic Inclined Curves In The Semi-Euclidean Space ¨ E^42. Applied Mathematics and Computation. 155(2), 2014, 373 – 389.
15. Turgut M, Yılmaz S. Smarandache Curves in Minkowski Spacetime. International Journal of Mathematical Combinatorics. 3,2008, 51 – 55.
16. Tuna A. The Serret-Frenet formulae for Quaternionic Curves In The Semi-Euclidean Spaces. Ph.D. Institute of Sciences, Sleyman Demirel University, 2002.