On Quaternionic Bertrand Curves in Euclidean $3$-Space

ISSN: 2148-1830
Yayın Aralığı: Yılda 2 Sayı
Başlangıç: 2013
Yayıncı: MATEMATİKÇİLER DERNEĞİ

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,

PDF

___

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.