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Year 2019, Volume: 2 Issue: 2, 119 - 125, 25.11.2019

Fatma Ateş

Abstract

References

  • [1] N. Ayy\i ld\i z , A. C. \c{C}\"{o}ken and Ahmet Y\"{u}cesan, \emph{A Characterization of Dual Lorentzian Spherical Curves in the Dual Lorentzian Space}, Taiwanese Journal of Mathematics, \textbf{11} (2007), 4, pp. 999-1018.
  • [2] R. A. Abdel Bakey, \emph{An Explicit Characterization of Dual Spherical Curve}, Commun. Fac. Sci. Univ. Ank. Series, \textbf{51} (2002), 2, pp. 1-9.
  • [3] M. Barros, A. Ferrández, P. Lucas, Meroño MA., \emph{General helices in the 3-dimensional Lorentzian space forms}, Rocky Mt J Math, \textbf{31}, (2001), pp. 373-388.
  • [4] S. Breuer, D. Gottlieb, \emph{Explicit Characterization of Spherical Curves}, Proc. Am. Math. Soc. \textbf{27} (1971), pp. 126-127.
  • [5] K. Ilarslan, \c{C}. Camci, H. Kocayigit, \emph{On the explicit characterization of spherical curves in 3-dimensional Lorentzian space}, Journal of Inverse and Ill-posed Problems, \textbf{11} (2003), 4, pp. 389-397.
  • [6] O. Kose, \emph{An Expilicit Characterization of Dual Spherical Curves}, Do\u{g}a Mat. \textbf{12} (1998), 3, pp. 105-113.
  • [7] H. Simsek, M. \"{O}zdemir, \emph{Generating hyperbolical rotation matrix for a given hyperboloid}, Linear Algebra Appl., \textbf{496} (2016), pp. 221-245.
  • [8] Z. Ozdemir, I. Gok, Y. Yayli, and F.N. Ekmekci, \emph{Notes on Magnetic Curves in 3D semi-Riemannian Manifolds}, Turk J Math., \textbf{39}, (2015), pp. 412-426.
  • [9] F. Ates, Z. \"{O}zdemir, \emph{Hyperbolic motions of a point on the general hyperboloid} (submitted).
  • [10] Y. C. Wong, \emph{On an Explicit Characterization of Spherical Curves}, Proc. Am. Math. Soc., \textbf{34} (1972), 1, pp. 239-242.
  • [11] Y. C. Wong, \emph{A global formulation of the condition for a curve to lie in a sphere}, Monatsh. Math. \textbf{67} (1963), pp. 363-365.

On Special Curves of General Hyperboloid in $ E_{1}^{3}$

Year 2019, Volume: 2 Issue: 2, 119 - 125, 25.11.2019

Fatma Ateş

Abstract

In this work, we give the Darboux vectors $\{\gamma \left( s\right) ,T\left( s\right) ,Y\left( s\right)\}$ of a given curve using the hyperbolically motion and hyperbolically inner product defined by Simsek and Özdemir in \cite{ozd}. Then, we present the variations of the geodesic curvature function $\kappa _{g}(s,w)$ and the speed function $v(s,w)$ of the curve $ \gamma $ at $w=0 $. Also, we define the new type curves whose Darboux frame vectors of a given curve makes a constant angle with the constant Killing vector field and also we obtain the parametric characterizations of these curves. At the end of this article, we exemplify these curves on the general hyperboloid with their figures using the program Mathematica.

Keywords

General hyperboloid Special curves Euclidean space Darboux frame

References

  • [1] N. Ayy\i ld\i z , A. C. \c{C}\"{o}ken and Ahmet Y\"{u}cesan, \emph{A Characterization of Dual Lorentzian Spherical Curves in the Dual Lorentzian Space}, Taiwanese Journal of Mathematics, \textbf{11} (2007), 4, pp. 999-1018.
  • [2] R. A. Abdel Bakey, \emph{An Explicit Characterization of Dual Spherical Curve}, Commun. Fac. Sci. Univ. Ank. Series, \textbf{51} (2002), 2, pp. 1-9.
  • [3] M. Barros, A. Ferrández, P. Lucas, Meroño MA., \emph{General helices in the 3-dimensional Lorentzian space forms}, Rocky Mt J Math, \textbf{31}, (2001), pp. 373-388.
  • [4] S. Breuer, D. Gottlieb, \emph{Explicit Characterization of Spherical Curves}, Proc. Am. Math. Soc. \textbf{27} (1971), pp. 126-127.
  • [5] K. Ilarslan, \c{C}. Camci, H. Kocayigit, \emph{On the explicit characterization of spherical curves in 3-dimensional Lorentzian space}, Journal of Inverse and Ill-posed Problems, \textbf{11} (2003), 4, pp. 389-397.
  • [6] O. Kose, \emph{An Expilicit Characterization of Dual Spherical Curves}, Do\u{g}a Mat. \textbf{12} (1998), 3, pp. 105-113.
  • [7] H. Simsek, M. \"{O}zdemir, \emph{Generating hyperbolical rotation matrix for a given hyperboloid}, Linear Algebra Appl., \textbf{496} (2016), pp. 221-245.
  • [8] Z. Ozdemir, I. Gok, Y. Yayli, and F.N. Ekmekci, \emph{Notes on Magnetic Curves in 3D semi-Riemannian Manifolds}, Turk J Math., \textbf{39}, (2015), pp. 412-426.
  • [9] F. Ates, Z. \"{O}zdemir, \emph{Hyperbolic motions of a point on the general hyperboloid} (submitted).
  • [10] Y. C. Wong, \emph{On an Explicit Characterization of Spherical Curves}, Proc. Am. Math. Soc., \textbf{34} (1972), 1, pp. 239-242.
  • [11] Y. C. Wong, \emph{A global formulation of the condition for a curve to lie in a sphere}, Monatsh. Math. \textbf{67} (1963), pp. 363-365.
There are 11 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Fatma Ateş 0000-0002-3529-1077

Publication Date November 25, 2019
Acceptance Date October 10, 2019
Published in Issue Year 2019 Volume: 2 Issue: 2

Cite

APA Ateş, F. (2019). On Special Curves of General Hyperboloid in $ E_{1}^{3}$. Conference Proceedings of Science and Technology, 2(2), 119-125.
AMA Ateş F. On Special Curves of General Hyperboloid in $ E_{1}^{3}$. Conference Proceedings of Science and Technology. November 2019;2(2):119-125.
Chicago Ateş, Fatma. “On Special Curves of General Hyperboloid in $ E_{1}^{3}$”. Conference Proceedings of Science and Technology 2, no. 2 (November 2019): 119-25.
EndNote Ateş F (November 1, 2019) On Special Curves of General Hyperboloid in $ E_{1}^{3}$. Conference Proceedings of Science and Technology 2 2 119–125.
IEEE F. Ateş, “On Special Curves of General Hyperboloid in $ E_{1}^{3}$”, Conference Proceedings of Science and Technology, vol. 2, no. 2, pp. 119–125, 2019.
ISNAD Ateş, Fatma. “On Special Curves of General Hyperboloid in $ E_{1}^{3}$”. Conference Proceedings of Science and Technology 2/2 (November 2019), 119-125.
JAMA Ateş F. On Special Curves of General Hyperboloid in $ E_{1}^{3}$. Conference Proceedings of Science and Technology. 2019;2:119–125.
MLA Ateş, Fatma. “On Special Curves of General Hyperboloid in $ E_{1}^{3}$”. Conference Proceedings of Science and Technology, vol. 2, no. 2, 2019, pp. 119-25.
Vancouver Ateş F. On Special Curves of General Hyperboloid in $ E_{1}^{3}$. Conference Proceedings of Science and Technology. 2019;2(2):119-25.
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