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Year 2020, Volume: 5 Issue: 2, 49 - 62, 31.10.2020

Abstract

References

  • Ali AT. Special Smarandache Curves in the Euclidean Space, International Journal of Mathematical Combinatorics. 2, 2010, 30 –36.
  • 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.
  • Demir S, Oztas¸ K. Serret-Frenet Formulas With Real Quaternions, Süleyman Demirel University Journal of Natural and Applied ¨ Sciences. 9(3), 2005, 1 – 7.
  • 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.
  • Hacısalihoglu HH. The Motion Geometry and Quatenions Theory (in Turkish), Gazi University Publications. 1983. ˘
  • 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.
  • Keilioglu O, İlarslan K. Quaternionic Bertrand Curves In Euclidean 4-Space. Bulletin of Mathematical Analysis and Applications. 5(3), 2013, 27 – 38.
  • Parlatıcı H. Quaternionic Smarandache Curves. Master Thesis. University of Sakarya, 2013.
  • Şenyurt S, ÇalıŞkan AS. An Application According to Spatial Quaternionic Smarandache Curve. Applied Mathematical Sciences. 9(5), 2015, 219 – 228.
  • Şenyurt S, Sivas S. An Application of Smarandache Curve. Ordu Univ. J. Sci. Tech. 3(1), (2013, 46 – 60.
  • 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.
  • Şenyurt S, Cevahir C, Altun Y. On Spatial Quaternionic Involute Curve A New View. Adv. Appl. Clifford Algebras. 27(2), 2017, 1815 – 1824.
  • 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).
  • 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.
  • Turgut M, Yılmaz S. Smarandache Curves in Minkowski Spacetime. International Journal of Mathematical Combinatorics. 3,2008, 51 – 55.
  • Tuna A. The Serret-Frenet formulae for Quaternionic Curves In The Semi-Euclidean Spaces. Ph.D. Institute of Sciences, Sleyman Demirel University, 2002.

Smarandache Curves of Spatial Quaternionic Bertrand Curve According to Frenet Frame

Year 2020, Volume: 5 Issue: 2, 49 - 62, 31.10.2020

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.

References

  • Ali AT. Special Smarandache Curves in the Euclidean Space, International Journal of Mathematical Combinatorics. 2, 2010, 30 –36.
  • 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.
  • Demir S, Oztas¸ K. Serret-Frenet Formulas With Real Quaternions, Süleyman Demirel University Journal of Natural and Applied ¨ Sciences. 9(3), 2005, 1 – 7.
  • 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.
  • Hacısalihoglu HH. The Motion Geometry and Quatenions Theory (in Turkish), Gazi University Publications. 1983. ˘
  • 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.
  • Keilioglu O, İlarslan K. Quaternionic Bertrand Curves In Euclidean 4-Space. Bulletin of Mathematical Analysis and Applications. 5(3), 2013, 27 – 38.
  • Parlatıcı H. Quaternionic Smarandache Curves. Master Thesis. University of Sakarya, 2013.
  • Şenyurt S, ÇalıŞkan AS. An Application According to Spatial Quaternionic Smarandache Curve. Applied Mathematical Sciences. 9(5), 2015, 219 – 228.
  • Şenyurt S, Sivas S. An Application of Smarandache Curve. Ordu Univ. J. Sci. Tech. 3(1), (2013, 46 – 60.
  • 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.
  • Şenyurt S, Cevahir C, Altun Y. On Spatial Quaternionic Involute Curve A New View. Adv. Appl. Clifford Algebras. 27(2), 2017, 1815 – 1824.
  • 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).
  • 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.
  • Turgut M, Yılmaz S. Smarandache Curves in Minkowski Spacetime. International Journal of Mathematical Combinatorics. 3,2008, 51 – 55.
  • Tuna A. The Serret-Frenet formulae for Quaternionic Curves In The Semi-Euclidean Spaces. Ph.D. Institute of Sciences, Sleyman Demirel University, 2002.
There are 16 citations in total.

Details

Primary Language English
Journal Section Volume V Issue II 2020
Authors

Süleyman Şenyurt

Ceyda Cevahir This is me

Yasin Altun This is me

Publication Date October 31, 2020
Published in Issue Year 2020 Volume: 5 Issue: 2

Cite

APA Şenyurt, S., Cevahir, C., & Altun, Y. (2020). Smarandache Curves of Spatial Quaternionic Bertrand Curve According to Frenet Frame. Turkish Journal of Science, 5(2), 49-62.
AMA Şenyurt S, Cevahir C, Altun Y. Smarandache Curves of Spatial Quaternionic Bertrand Curve According to Frenet Frame. TJOS. October 2020;5(2):49-62.
Chicago Şenyurt, Süleyman, Ceyda Cevahir, and Yasin Altun. “Smarandache Curves of Spatial Quaternionic Bertrand Curve According to Frenet Frame”. Turkish Journal of Science 5, no. 2 (October 2020): 49-62.
EndNote Şenyurt S, Cevahir C, Altun Y (October 1, 2020) Smarandache Curves of Spatial Quaternionic Bertrand Curve According to Frenet Frame. Turkish Journal of Science 5 2 49–62.
IEEE S. Şenyurt, C. Cevahir, and Y. Altun, “Smarandache Curves of Spatial Quaternionic Bertrand Curve According to Frenet Frame”, TJOS, vol. 5, no. 2, pp. 49–62, 2020.
ISNAD Şenyurt, Süleyman et al. “Smarandache Curves of Spatial Quaternionic Bertrand Curve According to Frenet Frame”. Turkish Journal of Science 5/2 (October 2020), 49-62.
JAMA Şenyurt S, Cevahir C, Altun Y. Smarandache Curves of Spatial Quaternionic Bertrand Curve According to Frenet Frame. TJOS. 2020;5:49–62.
MLA Şenyurt, Süleyman et al. “Smarandache Curves of Spatial Quaternionic Bertrand Curve According to Frenet Frame”. Turkish Journal of Science, vol. 5, no. 2, 2020, pp. 49-62.
Vancouver Şenyurt S, Cevahir C, Altun Y. Smarandache Curves of Spatial Quaternionic Bertrand Curve According to Frenet Frame. TJOS. 2020;5(2):49-62.