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Year 2022, Volume: 14 Issue: 2, 355 - 365, 30.12.2022
https://doi.org/10.47000/tjmcs.1021801

Abstract

References

  • Bharathi, K., Nagaraj, M., Quaternion valued function of a real Serret-Frenet formulae, Indian J. Pure Appl. Math., 16(1985), 741–756.
  • Bioche, C.H., Sur les courbes de M. Bertrand, Bulletin de la Soci´et´e Math´ematique de France, 17(1889), 109–112.
  • Burke, F.J., Bertrand curves associated with a pair of curves, Mathematics Magazine, 34(1960), 60–62.
  • Çöken, A.C., Tuna, A., On the quaternionic inclined curves in the semi-Euclidean space E4 2, Applied Mathematics and Computation, 155(2004), 373–389.
  • Hacısalioğlu, H.H., Hareket Geometrisi ve Kuaterniyonlar Teorisi, Ankara, Tukey, 1983.
  • Hamilton, W.R., Element of Quaternions I, II and III, Chelsea, 1899.
  • O’Neill, B., Semi-Riemannian Geometry with Applications to Relativity, New York, USA, 1983.
  • Sabuncuo˘glu A., Diferansiyel Geometri, Nobel Academic Publishing, Ankara, 2014.
  • Tuna, A., Serret Frenet Formulae for Quaternionic Curves in Semi Euclidean Space, Master Thesis, Süleyman Demirel University, 2002.
  • Ward, J.P., Quaternions and Cayley Numbers, London, 1997.

On Quaternionic Bertrand Curves in Euclidean $3$-Space

Year 2022, Volume: 14 Issue: 2, 355 - 365, 30.12.2022
https://doi.org/10.47000/tjmcs.1021801

Abstract

In this article, spatial quaternionic Bertrand curve pairs in the 3-dimensional Euclidean space are examined. Algebraic properties of quaternions, basic definitions and theorems are given. Later, some characterizations of spatial quaternionic Bertrand curve pairs are obtained in the 3-dimensional Euclidean space.

References

  • Bharathi, K., Nagaraj, M., Quaternion valued function of a real Serret-Frenet formulae, Indian J. Pure Appl. Math., 16(1985), 741–756.
  • Bioche, C.H., Sur les courbes de M. Bertrand, Bulletin de la Soci´et´e Math´ematique de France, 17(1889), 109–112.
  • Burke, F.J., Bertrand curves associated with a pair of curves, Mathematics Magazine, 34(1960), 60–62.
  • Çöken, A.C., Tuna, A., On the quaternionic inclined curves in the semi-Euclidean space E4 2, Applied Mathematics and Computation, 155(2004), 373–389.
  • Hacısalioğlu, H.H., Hareket Geometrisi ve Kuaterniyonlar Teorisi, Ankara, Tukey, 1983.
  • Hamilton, W.R., Element of Quaternions I, II and III, Chelsea, 1899.
  • O’Neill, B., Semi-Riemannian Geometry with Applications to Relativity, New York, USA, 1983.
  • Sabuncuo˘glu A., Diferansiyel Geometri, Nobel Academic Publishing, Ankara, 2014.
  • Tuna, A., Serret Frenet Formulae for Quaternionic Curves in Semi Euclidean Space, Master Thesis, Süleyman Demirel University, 2002.
  • Ward, J.P., Quaternions and Cayley Numbers, London, 1997.
There are 10 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Aykut Has 0000-0003-0658-9365

Beyhan Yılmaz 0000-0002-5091-3487

Early Pub Date December 23, 2022
Publication Date December 30, 2022
Published in Issue Year 2022 Volume: 14 Issue: 2

Cite

APA Has, A., & Yılmaz, B. (2022). On Quaternionic Bertrand Curves in Euclidean $3$-Space. Turkish Journal of Mathematics and Computer Science, 14(2), 355-365. https://doi.org/10.47000/tjmcs.1021801
AMA Has A, Yılmaz B. On Quaternionic Bertrand Curves in Euclidean $3$-Space. TJMCS. December 2022;14(2):355-365. doi:10.47000/tjmcs.1021801
Chicago Has, Aykut, and Beyhan Yılmaz. “On Quaternionic Bertrand Curves in Euclidean $3$-Space”. Turkish Journal of Mathematics and Computer Science 14, no. 2 (December 2022): 355-65. https://doi.org/10.47000/tjmcs.1021801.
EndNote Has A, Yılmaz B (December 1, 2022) On Quaternionic Bertrand Curves in Euclidean $3$-Space. Turkish Journal of Mathematics and Computer Science 14 2 355–365.
IEEE A. Has and B. Yılmaz, “On Quaternionic Bertrand Curves in Euclidean $3$-Space”, TJMCS, vol. 14, no. 2, pp. 355–365, 2022, doi: 10.47000/tjmcs.1021801.
ISNAD Has, Aykut - Yılmaz, Beyhan. “On Quaternionic Bertrand Curves in Euclidean $3$-Space”. Turkish Journal of Mathematics and Computer Science 14/2 (December 2022), 355-365. https://doi.org/10.47000/tjmcs.1021801.
JAMA Has A, Yılmaz B. On Quaternionic Bertrand Curves in Euclidean $3$-Space. TJMCS. 2022;14:355–365.
MLA Has, Aykut and Beyhan Yılmaz. “On Quaternionic Bertrand Curves in Euclidean $3$-Space”. Turkish Journal of Mathematics and Computer Science, vol. 14, no. 2, 2022, pp. 355-6, doi:10.47000/tjmcs.1021801.
Vancouver Has A, Yılmaz B. On Quaternionic Bertrand Curves in Euclidean $3$-Space. TJMCS. 2022;14(2):355-6.

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