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
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.
Keywords
Quaternions spatial quaternion quaternion algebra Bertrand curve curvatures 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.
Details
| Primary Language | English |
|---|---|
| Subjects | Mathematical Sciences |
| Journal Section | Articles |
| Authors | |
| Early Pub Date | December 23, 2022 |
| Publication Date | December 30, 2022 |
| Published in Issue | Year 2022 Volume: 14 Issue: 2 |