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Year 2023, Volume: 11 Issue: 1, 40 - 45, 30.04.2023

Ameth Ndiaye , Fatih Doğan

Abstract

References

  • [1] M. Brozos-V´azquez, E. Garc´ıa-Rio, P. Gilkey, S. Nikevi´c and R, V´azquez-Lorenzo, The Geometry of Walker Manifolds, Synthesis Lectures on Mathematics and Statistics, 5. Morgan and Claypool Publishers, Williston, VT, 2009.
  • [2] M. P. do Carmo, Differential geometry of curves and surfaces, Prentice-Hall, Inc., Englewood Cliffs, N.J., viii+503 pp. 190-191.
  • [3] F. Do ˇ gan and Y. Yaylı, On isophote curves and their characterizations, Turkish J. Math., 39, 650–664, 2015
  • [4] F. Do ˇ gan and Y. Yaylı, Isophote curves on spacelike surfaces in Lorentz-Minkowski space E3 1 , Asian-Eur. J. Math., 14, (10), 2150180, (2021).
  • [5] F. Do ˇ gan, Isophote curves on timelike surfaces in Minkowski 3-space, An. S¸ tiint¸. Univ. Al. I. Cuza Ias¸i. Mat. (N.S.) 63, (1), 133-143, (2017).
  • [6] A. Ndiaye, M. Gningue, H. Dathe, Darboux curves in three dimensional Walker manifold, Glob. J. Adv. Res. Class. Mod. Geom., 11, (1), 45–50 (2022).
  • [7] M. Gningue, A. Ndiaye, R. Nkunzimana, Biharmonic curves in a strict Walker 3-manifold, Int. J. Math. Math. Sci., Art. ID 3855033, 6 pp (2022).
  • [8] A. Niang, A. Ndiaye, A. S. Diallo, A Classification of Strict Walker 3-Manifold, Konuralp J. Math., (2021), 9(1), 148-153.
  • [9] Z. O¨ zdemir, G. Cansu, Y. Yaylı, Kinematic modeling of Rytov’s law and electromagnetic curves in the optical fiber based on elliptical quaternion algebra, Optik - International Journal for Light and Electron Optics. Doi:https://dx.doi.org/10.1016/j.ijleo.2021.166334
  • [10] Z. K. Y¨ uzbası; D.W. Yoon, On geometry of isophote curves in Galilean space, AIMS Math. 6, (1), 66–76, (2021).

Isophote Curves in a Strict Walker 3-Manifold and Application in Optical Fiber

Year 2023, Volume: 11 Issue: 1, 40 - 45, 30.04.2023

Ameth Ndiaye , Fatih Doğan

Abstract

In this paper, we introduice and investigate the geometry of isophote curves in a strict Walker 3-manifold using the Darboux frame. We give some characterisations about isophote and its axis and we give an application about optical fiber and its polarization vector.

Keywords

Curves Isophote curve Walker manifolds.

References

  • [1] M. Brozos-V´azquez, E. Garc´ıa-Rio, P. Gilkey, S. Nikevi´c and R, V´azquez-Lorenzo, The Geometry of Walker Manifolds, Synthesis Lectures on Mathematics and Statistics, 5. Morgan and Claypool Publishers, Williston, VT, 2009.
  • [2] M. P. do Carmo, Differential geometry of curves and surfaces, Prentice-Hall, Inc., Englewood Cliffs, N.J., viii+503 pp. 190-191.
  • [3] F. Do ˇ gan and Y. Yaylı, On isophote curves and their characterizations, Turkish J. Math., 39, 650–664, 2015
  • [4] F. Do ˇ gan and Y. Yaylı, Isophote curves on spacelike surfaces in Lorentz-Minkowski space E3 1 , Asian-Eur. J. Math., 14, (10), 2150180, (2021).
  • [5] F. Do ˇ gan, Isophote curves on timelike surfaces in Minkowski 3-space, An. S¸ tiint¸. Univ. Al. I. Cuza Ias¸i. Mat. (N.S.) 63, (1), 133-143, (2017).
  • [6] A. Ndiaye, M. Gningue, H. Dathe, Darboux curves in three dimensional Walker manifold, Glob. J. Adv. Res. Class. Mod. Geom., 11, (1), 45–50 (2022).
  • [7] M. Gningue, A. Ndiaye, R. Nkunzimana, Biharmonic curves in a strict Walker 3-manifold, Int. J. Math. Math. Sci., Art. ID 3855033, 6 pp (2022).
  • [8] A. Niang, A. Ndiaye, A. S. Diallo, A Classification of Strict Walker 3-Manifold, Konuralp J. Math., (2021), 9(1), 148-153.
  • [9] Z. O¨ zdemir, G. Cansu, Y. Yaylı, Kinematic modeling of Rytov’s law and electromagnetic curves in the optical fiber based on elliptical quaternion algebra, Optik - International Journal for Light and Electron Optics. Doi:https://dx.doi.org/10.1016/j.ijleo.2021.166334
  • [10] Z. K. Y¨ uzbası; D.W. Yoon, On geometry of isophote curves in Galilean space, AIMS Math. 6, (1), 66–76, (2021).
There are 10 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Ameth Ndiaye

Fatih Doğan

Publication Date April 30, 2023
Submission Date February 25, 2022
Acceptance Date December 18, 2022
Published in Issue Year 2023 Volume: 11 Issue: 1

Cite

APA Ndiaye, A., & Doğan, F. (2023). Isophote Curves in a Strict Walker 3-Manifold and Application in Optical Fiber. Konuralp Journal of Mathematics, 11(1), 40-45.
AMA Ndiaye A, Doğan F. Isophote Curves in a Strict Walker 3-Manifold and Application in Optical Fiber. Konuralp J. Math. April 2023;11(1):40-45.
Chicago Ndiaye, Ameth, and Fatih Doğan. “Isophote Curves in a Strict Walker 3-Manifold and Application in Optical Fiber”. Konuralp Journal of Mathematics 11, no. 1 (April 2023): 40-45.
EndNote Ndiaye A, Doğan F (April 1, 2023) Isophote Curves in a Strict Walker 3-Manifold and Application in Optical Fiber. Konuralp Journal of Mathematics 11 1 40–45.
IEEE A. Ndiaye and F. Doğan, “Isophote Curves in a Strict Walker 3-Manifold and Application in Optical Fiber”, Konuralp J. Math., vol. 11, no. 1, pp. 40–45, 2023.
ISNAD Ndiaye, Ameth - Doğan, Fatih. “Isophote Curves in a Strict Walker 3-Manifold and Application in Optical Fiber”. Konuralp Journal of Mathematics 11/1 (April 2023), 40-45.
JAMA Ndiaye A, Doğan F. Isophote Curves in a Strict Walker 3-Manifold and Application in Optical Fiber. Konuralp J. Math. 2023;11:40–45.
MLA Ndiaye, Ameth and Fatih Doğan. “Isophote Curves in a Strict Walker 3-Manifold and Application in Optical Fiber”. Konuralp Journal of Mathematics, vol. 11, no. 1, 2023, pp. 40-45.
Vancouver Ndiaye A, Doğan F. Isophote Curves in a Strict Walker 3-Manifold and Application in Optical Fiber. Konuralp J. Math. 2023;11(1):40-5.
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