On the quaternionic Bertrand curves of AW k -type in Euclidean space E³
On the quaternionic Bertrand curves of AW k -type in Euclidean space E³
In this paper, We consider that the curvature conditions of AW k -type 1 ≤k≤ 3 quaternioniccurves in Euclidean space E3and investigates quaternionic Bertrand curves α : I → Q with k 6= 0and r 6= 0. Besides, we show that quaternionic Bertrand curves to be AW 2 -type and AW 3 -typequaternionic curves in E. But it is shown that there is no such a quaternionic Bertrand curve ofAW 1 -type
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- [1] A. C. C¸ ¨oken, A. Tuna, On the quaternionic inclined curves in the semi-Euclidean space E4 2 , Appl. Math. Computation, 155, (2004), 373-389.
- [2] C. Ozg¨ur, F. Gezgin, On some curves of AW(k)-type, Differ. Geom. Dyn. Syst, 7, (2005) , 74–80. ¨
- [3] C¸ . Camcı, K. ˙Ilarslan, L. Kula, H.H. Hacısaliho˘glu, Harmonic curvatures and generalized helices in En, Chaos Solitons & Fractals, (2009), 40(5):2590–6.
- [4] E. Ata, Y. Yaylı, Dual quaternions and dual projective spaces, Chaos Solitons & Fractals 40, (2009), 15(3):1255-1263.
- [5] E. Ata, Y. Yaylı, Split quaternions and semi-Euclidean projective spaces, Chaos Solitons & Fractals 41, (2009), 30(4):1910-1915.
- [6] F. Kahraman, ˙I. G¨ok, H.H. Hacısaliho˘glu, On the quaternionic B2-Slant Helices in the semi-Euclidean Space E4 2 , Appl. Math. Computation, 218, (2012), 6391-6400.
- [7] ˙I. G¨ok ˙I, O. Z. Okuyucu, F. Kahraman and H. H. Hacisaliho˘glu, On the Quaternionic B2-Slant Helices in the Euclidean Space E4 , Adv. Appl. Clifford Algebras, 21 (2011), 707–719.
- [8] K. Arslan, C. Ozg¨ur, Curves and surfaces of AW(k)-type, Geometry and Topology of Submanifolds, ¨ IX (Valenciennes/Lyan/Leuven,1997), World. Sci. Publishing, River Edge, NJ, (1999), pp. 21–26.
- [9] K. Bharathi, M. Nagaraj, Quaternion valued function of a real Serret-Frenet formulae, Indian J. Pure Appl. Math, 16, (1985), 741-756.
- [10] M. Karada˘g, A.˙I. Sivrida˘g, Kuaterniyonik E˘gilim C¸ izgileri i¸cin karakterizasyonlar, Erc. Unv. Fen ¨ Bil. Derg. 13 1-2, (1997), 37-53.
- [11] M. K¨ulahcı, M. Bektas, M. Erg¨ut, Curves of AW(k)-type in 3-dimensional null cone, Physics Letters A 371, (2007), 275-277.
- [12] M. K¨ulahcı, M. Bektas, M. Erg¨ut, On harmonic curvatures of a Frenet curve in Lorentzian space, Chaos Solitons & Fractals 41, (2009), 1668–1675.
- [13] S. Izumiya, N. Takeuchi, Generic properties of helices and Bertrand curves, J. Geom., 74, (2002), 97–109.
- [14] S. Izumiya, N. Takeuchi, New special curves and developable surfaces, Turkish J. Math., 28 (2), (2004), 153–163.
- [15] S. Kızıltu˘g, Y. Yaylı, Bertrand curves of AW(k)-type in according to the Equiform Geometry of the Galilean Space, Abstract and Applied Analysis Volume, (2014), Article ID 402360, 6 pages. [16] S. Kızıltu˘g, Y. Yaylı, On the quaternionic Mannheim curves of Aw(k)-type in Euclidean space E3 42(2), (2015).
- ISSN: 2636-8714
- Başlangıç: 2019
- Yayıncı: Seyfullah HIZARCI