Öz
Kaynakça
- [1] N. Ayyıldız , A. C. Çöken and Ahmet Yücesan, A Characterization of Dual Lorentzian Spherical Curves in the Dual Lorentzian Space, Taiwanese Journal of Mathematics, 11(4) (2007), 999-1018.
- [2] R. A. Abdel Bakey, An Explicit Characterization of Dual Spherical Curve, Commun. Fac. Sci. Univ. Ank. Series, 51(2) (2002), 2, 1-9
- [3] S. Breuer, D. Gottlieb, Explicit Characterization of Spherical Curves, Proc. Am. Math. Soc. 27 (1971), 126-127.
- [4] K. Ilarslan, Ç. Camci, H. Kocayigit, On the explicit characterization of spherical curves in 3-dimensional Lorentzian space, Journal of Inverse and Ill-posed Problems, 11 (2003), 4, pp. 389-397.
- [5] S. Izumiya, N. Takeuchi, New Special Curves and Developable Surfaces, Turk. J. Math. 28 (2004), 153-163.
- [6] O. Kose, An Expilicit Characterization of Dual Spherical Curves, Do˘ga Mat. 12(3) (1998), 105-113.
- [7] M. Özdemir, An Alternative Approach to Elliptical Motion, Adv. Appl. Clifford Algebras 26 (2016), 279-304.
- [8] Z. Özdemir, F. Ates, Trajectories of a point on the elliptical 2-sphere, arXiv:submit/2795112.
- [9] P. D. Scofield, Curves of Constant Precession, Amer. Math. Monthly. 102(6)(1995), 531-537.
- [10] Y. C. Wong, On an Explicit Characterization of Spherical Curves, Proc. Am. Math. Soc., 34(1) (1972), 239-242.
- [11] Y. C. Wong, A global formulation of the condition for a curve to lie in a sphere, Monatsh. Math. 67 (1963), 363-365.
Öz
In this study, we investigate three types of special helices whose axis is a fixed constant Killing vector field on the Ellipsoid $% \mathbb{S}_{a_{1},a_{2},a_{3}}^{2}$ in $\mathbb{R}_{a_{1},a_{2},a_{3}}^{3}$. Then, we obtain the curvatures of all special helices on the ellipsoid $% \mathbb{S}_{a_{1},a_{2},a_{3}}^{2}$ and give some characterizations of these curves. Moreover, we present various examples and visualize their images using the Mathematica program.
Anahtar Kelimeler
Frame fields Killing vector field Special curves and surfaces.
Kaynakça
- [1] N. Ayyıldız , A. C. Çöken and Ahmet Yücesan, A Characterization of Dual Lorentzian Spherical Curves in the Dual Lorentzian Space, Taiwanese Journal of Mathematics, 11(4) (2007), 999-1018.
- [2] R. A. Abdel Bakey, An Explicit Characterization of Dual Spherical Curve, Commun. Fac. Sci. Univ. Ank. Series, 51(2) (2002), 2, 1-9
- [3] S. Breuer, D. Gottlieb, Explicit Characterization of Spherical Curves, Proc. Am. Math. Soc. 27 (1971), 126-127.
- [4] K. Ilarslan, Ç. Camci, H. Kocayigit, On the explicit characterization of spherical curves in 3-dimensional Lorentzian space, Journal of Inverse and Ill-posed Problems, 11 (2003), 4, pp. 389-397.
- [5] S. Izumiya, N. Takeuchi, New Special Curves and Developable Surfaces, Turk. J. Math. 28 (2004), 153-163.
- [6] O. Kose, An Expilicit Characterization of Dual Spherical Curves, Do˘ga Mat. 12(3) (1998), 105-113.
- [7] M. Özdemir, An Alternative Approach to Elliptical Motion, Adv. Appl. Clifford Algebras 26 (2016), 279-304.
- [8] Z. Özdemir, F. Ates, Trajectories of a point on the elliptical 2-sphere, arXiv:submit/2795112.
- [9] P. D. Scofield, Curves of Constant Precession, Amer. Math. Monthly. 102(6)(1995), 531-537.
- [10] Y. C. Wong, On an Explicit Characterization of Spherical Curves, Proc. Am. Math. Soc., 34(1) (1972), 239-242.
- [11] Y. C. Wong, A global formulation of the condition for a curve to lie in a sphere, Monatsh. Math. 67 (1963), 363-365.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Mühendislik |
| Bölüm | Articles |
| Yazarlar | |
| Yayımlanma Tarihi | 25 Kasım 2019 |
| Kabul Tarihi | 25 Ekim 2019 |
| Yayımlandığı Sayı | Yıl 2019 Cilt: 2 Sayı: 2 |
