Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
권호 표지
DOI QR코드

DOI QR Code

TIMELIKE HELICES IN THE SEMI-EUCLIDEAN SPACE E42

  • Received : 2021.04.01
  • Accepted : 2022.07.19
  • Published : 2022.09.01
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, we define timelike curves in R42 and characterize such curves in terms of Frenet frame. Also, we examine the timelike helices of R42, taking into account their curvatures. In addition, we study timelike slant helices, timelike B1-slant helices, timelike B2-slant helices in four dimensional semi-Euclidean space, R42. And then we obtain an approximate solution for the timelike B1 slant helix with Taylor matrix collocation method.

Keywords

References

  1. T. A. Ahmad and R. Lopez, Slant helices in Euclidean 4-space E4, preprint (2009); arXiv:0901.3324.
  2. B. Altunkaya, Helices in the n-dimensional Minkowski spacetime, Results in Phy. 14 (2019), 102445. https://doi.org/10.1016/j.rinp.2019.102445
  3. R. Ayazoglu, S. S. Sener, and T. A. Aydin, Existence of solutions for a resonant problem under Landesman-Lazer type conditions involving more general elliptic operators in divergence form, Trans. Nat. Aca. Sci. Azer. Ser. Phys.-tech. Math. Sci. 40 (2020), 1-14.
  4. T. A. Aydin and M. Sezer, Taylor-Matrix Collocation Method to Solution of Differential Equations Characterizing Spherical Curves in Euclidean 4-Space, Celal Bayar Uni. J. Sci. 15 (2019), 1-7.
  5. T. A. Aydin, M. Sezer, and H. Kocayigit, An Approximate Solution of Equations Characterizing Spacelike Curves of Constant Breadth in Minkowski 3-Space, New Trend in Math. Sci. 6 (2018), 182-195.
  6. A. C. Coken and A. Gorgulu, On Joachimsthal's theorems in semi-Euclidean spaces, Nonlinear Analysis: Theory, Meth. App. 70 (2009), 3932-3942. https://doi.org/10.1016/j.na.2008.08.003
  7. I. Gok, C. Camci, and H. H. Hacisalihoglu, Vn-slant helices in Euclidean n-space En, Math. Commun. 14 (2009), 317-329.
  8. M. Hosaka, Theory of Curves. Modeling of Curves and Surfaces in CAD/CAM. Computer Graphics-Systems and Applications, Springer, Berlin, Heidelberg, 1992.
  9. S. Izumiya and N. Takeuchi, New special curves and developable surfaces, Turk. J. Math. 28 (2004), 153-163.
  10. F. Kahraman, I. Gok, and H. H. Hacisalihoglu, On the quaternionic B2 slant helices in the semi-Euclidean space E42, App. Math. Comp. 218 (2012), 6391-6400. https://doi.org/10.1016/j.amc.2011.12.007
  11. F. Klein and S. Lie, Uber diejenigen ebenenen kurven welche durch ein geschlossenes system von einfach unendlich vielen vartauschbaren linearen transformationen in sich ubergehen, Math. Ann. 4 (1871), 50-84. https://doi.org/10.1007/BF01443297
  12. L. Kula and Y. Yayli, On slant helix and its spherical indicatrix, Appl. Math. Comput. 169 (2005), 600-607.
  13. R. A. Mashiyev, Three Solutions to a Neumann Problem for Elliptic Equations with Variable Exponent, Arab. J. Sci. Eng. 36 (2011), 1559-1567. https://doi.org/10.1007/s13369-011-0141-x
  14. J. Monterde, Curves With Constant Curvature Ratios, Bol. Soc. Mat. Mex. 13 (2007), 177-186.
  15. M. Onder, M. Kazaz, H. Kocayigit, and O. Kilic, B2-slant helix in Euclidean 4-space E4, Int. J. Cont. Math. Sci. 3 (2008), 1433-1440.
  16. B. O'Neill, Semi-Riemannian Geometry with Applications to Relativity, Academic Press Inc., London, 1983.
  17. G. Ozturk, K. Arslan, and H. H. Hacisalihoglu, A characterization of ccr-curves in Rm, Proc. Estonian Acad. Sci. 57 (2008), 217-224. https://doi.org/10.3176/proc.2008.4.03
  18. V. Rovenski, Geometry of curves and surfaces with maple, Birkhauser, London, 2000.
  19. E. Soley and M. Tosun, Timelike Bertrand Curves in Semi-Euclidean Space, Int. J. Math. Stat. 14 (2013), 78-89.