Research Article
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Timelike V-Bertrand Curves in Minkowski 3-Space $E_{1}^{3}$

Year 2022, Issue: 38, 14 - 24, 31.03.2022

Burhan Bilgin Çetin Camcı

https://doi.org/10.53570/jnt.1051013

Abstract

In this paper, the timelike V-Bertrand curve, a new type Bertrand curve in Minkowski 3-Space $E_{1}^{3}$, is characterized. Based on the timelike V-Bertrand curve, the properties of the timelike T, N, and B Bertrand curves are obtained. From the timelike V-Bertrand curve, f-Bertrand curves and Bertrand surfaces are defined. We support the existence of these new curves and surfaces with examples. Finally, we discuss the results for further research.

Keywords

Bertrand curves V-Bertrand curves Minkowski 3-space timelike V-Bertrand curves

Supporting Institution

Office of Scientific Research Projects Coordination at Çanakkale Onsekiz Mart University

Project Number

FYL-2019-2927

Thanks

This work was supported by the Office of Scientific Research Projects Coordination at Çanakkale Onsekiz Mart University, Grant number: FYL-2019-2927.

References

  • J. Bertrand, Memoire Sur La Theorie Des Courbes a Double Courbure, Journal de Mathématiques Pures et Appliquées 15 (1850) 332–350.
  • J. A. Serret, Sur Quelquees Formules Relatives À La Thérie De Courbes À Double Courbure, Journal de Mathématiques Pures et Appliquées 16 (1851) 193-207.
  • D. J. Struik, Lectures on Classical Differential Geometry, Dover Publications, 2nd Edition, 1950.
  • S. Izumiya, N. Tkeuchi, Generic Properties of Helices and Bertrand Curves, Journal of Geometry 74 (1-2) (2002) 97–109.
  • Ç. Camcı, A. Uçum, K. İlarslan, A New Approach to Bertrand Curves in Euclidean 3-space, Journal of Geometry 111 (3) (2020) 1–15.
  • K. İlarslan, A. Uçum, N. Kılıç Aslan, E. Nešović, Note On Bertrand B-Pairs of Curves in Minkowski 3-Space, Honam Mathematical Journal 40 (3) (2018) 561–576.
  • A. Uçum, O. Keçilioğlu, K. İlarslan, Generalized Bertrand Curves with Timelike (1,3)-normal Plane in Minkowski Space-time, Kuwait Journal of Science 42 (3) (2015) 10–27.
  • H. Matsuda, S. Yorozu, Notes on Bertrand Curves, Yokohama Mathematical Journal 50 (2003) 41–58.
  • P. Lucas, J. A. Ortega-Yagües, Bertrand Curves in the Three-dimensional Sphere, Journal of Geometry and Physics 62 (2012) 1903–1914.
  • M. Dede, C. Ekici, İ. Arslan Güven, Directional Bertrand Curves, Journal of Science 31 (1) (2018) 202-2011.
  • Ç. Camcı, On a New Type Bertrand Curve, (2020) pages 18. arXiv:2001.02298.
  • B. Bilgin, V -Bertrand Curve Mates in Minkowski 3-Space, Master’s of Thesis, Çanakkale Onsekiz Mart University (2020) Çanakkale, Turkey.
  • W. Kuhnel, Differential Geometry: Curves-Surfaces-Manifolds, Braunschweig, Wiesbaden, 1999.
  • A. Uçum, K. İlarslan, On Timelike Bertrand Curves in Minkowski 3-Space, Honam Mathematical Journal 38 (3) (2016) 467–477.

Year 2022, Issue: 38, 14 - 24, 31.03.2022

Burhan Bilgin Çetin Camcı

https://doi.org/10.53570/jnt.1051013

Abstract

Project Number

FYL-2019-2927

References

  • J. Bertrand, Memoire Sur La Theorie Des Courbes a Double Courbure, Journal de Mathématiques Pures et Appliquées 15 (1850) 332–350.
  • J. A. Serret, Sur Quelquees Formules Relatives À La Thérie De Courbes À Double Courbure, Journal de Mathématiques Pures et Appliquées 16 (1851) 193-207.
  • D. J. Struik, Lectures on Classical Differential Geometry, Dover Publications, 2nd Edition, 1950.
  • S. Izumiya, N. Tkeuchi, Generic Properties of Helices and Bertrand Curves, Journal of Geometry 74 (1-2) (2002) 97–109.
  • Ç. Camcı, A. Uçum, K. İlarslan, A New Approach to Bertrand Curves in Euclidean 3-space, Journal of Geometry 111 (3) (2020) 1–15.
  • K. İlarslan, A. Uçum, N. Kılıç Aslan, E. Nešović, Note On Bertrand B-Pairs of Curves in Minkowski 3-Space, Honam Mathematical Journal 40 (3) (2018) 561–576.
  • A. Uçum, O. Keçilioğlu, K. İlarslan, Generalized Bertrand Curves with Timelike (1,3)-normal Plane in Minkowski Space-time, Kuwait Journal of Science 42 (3) (2015) 10–27.
  • H. Matsuda, S. Yorozu, Notes on Bertrand Curves, Yokohama Mathematical Journal 50 (2003) 41–58.
  • P. Lucas, J. A. Ortega-Yagües, Bertrand Curves in the Three-dimensional Sphere, Journal of Geometry and Physics 62 (2012) 1903–1914.
  • M. Dede, C. Ekici, İ. Arslan Güven, Directional Bertrand Curves, Journal of Science 31 (1) (2018) 202-2011.
  • Ç. Camcı, On a New Type Bertrand Curve, (2020) pages 18. arXiv:2001.02298.
  • B. Bilgin, V -Bertrand Curve Mates in Minkowski 3-Space, Master’s of Thesis, Çanakkale Onsekiz Mart University (2020) Çanakkale, Turkey.
  • W. Kuhnel, Differential Geometry: Curves-Surfaces-Manifolds, Braunschweig, Wiesbaden, 1999.
  • A. Uçum, K. İlarslan, On Timelike Bertrand Curves in Minkowski 3-Space, Honam Mathematical Journal 38 (3) (2016) 467–477.
There are 14 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Article
Authors

Burhan Bilgin 0000-0002-3181-2031

Çetin Camcı 0000-0002-0122-559X

Project Number FYL-2019-2927
Publication Date March 31, 2022
Submission Date December 30, 2021
Published in Issue Year 2022 Issue: 38

Cite

APA Bilgin, B., & Camcı, Ç. (2022). Timelike V-Bertrand Curves in Minkowski 3-Space $E_{1}^{3}$. Journal of New Theory(38), 14-24. https://doi.org/10.53570/jnt.1051013
AMA Bilgin B, Camcı Ç. Timelike V-Bertrand Curves in Minkowski 3-Space $E_{1}^{3}$. JNT. March 2022;(38):14-24. doi:10.53570/jnt.1051013
Chicago Bilgin, Burhan, and Çetin Camcı. “Timelike V-Bertrand Curves in Minkowski 3-Space $E_{1}^{3}$”. Journal of New Theory, no. 38 (March 2022): 14-24. https://doi.org/10.53570/jnt.1051013.
EndNote Bilgin B, Camcı Ç (March 1, 2022) Timelike V-Bertrand Curves in Minkowski 3-Space $E_{1}^{3}$. Journal of New Theory 38 14–24.
IEEE B. Bilgin and Ç. Camcı, “Timelike V-Bertrand Curves in Minkowski 3-Space $E_{1}^{3}$”, JNT, no. 38, pp. 14–24, March 2022, doi: 10.53570/jnt.1051013.
ISNAD Bilgin, Burhan - Camcı, Çetin. “Timelike V-Bertrand Curves in Minkowski 3-Space $E_{1}^{3}$”. Journal of New Theory 38 (March 2022), 14-24. https://doi.org/10.53570/jnt.1051013.
JAMA Bilgin B, Camcı Ç. Timelike V-Bertrand Curves in Minkowski 3-Space $E_{1}^{3}$. JNT. 2022;:14–24.
MLA Bilgin, Burhan and Çetin Camcı. “Timelike V-Bertrand Curves in Minkowski 3-Space $E_{1}^{3}$”. Journal of New Theory, no. 38, 2022, pp. 14-24, doi:10.53570/jnt.1051013.
Vancouver Bilgin B, Camcı Ç. Timelike V-Bertrand Curves in Minkowski 3-Space $E_{1}^{3}$. JNT. 2022(38):14-2.
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