Araştırma Makalesi
BibTex RIS Kaynak Göster

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

Yıl 2022, Sayı: 38, 14 - 24, 31.03.2022

Burhan Bilgin Çetin Camcı

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

Öz

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.

Anahtar Kelimeler

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

Destekleyen Kurum

Office of Scientific Research Projects Coordination at Çanakkale Onsekiz Mart University

Proje Numarası

FYL-2019-2927

Teşekkür

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

Kaynakça

  • 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.

Yıl 2022, Sayı: 38, 14 - 24, 31.03.2022

Burhan Bilgin Çetin Camcı

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

Öz

Proje Numarası

FYL-2019-2927

Kaynakça

  • 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.
Toplam 14 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Araştırma Makalesi
Yazarlar

Burhan Bilgin 0000-0002-3181-2031

Çetin Camcı 0000-0002-0122-559X

Proje Numarası FYL-2019-2927
Yayımlanma Tarihi 31 Mart 2022
Gönderilme Tarihi 30 Aralık 2021
Yayımlandığı Sayı Yıl 2022 Sayı: 38

Kaynak Göster

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. Mart 2022;(38):14-24. doi:10.53570/jnt.1051013
Chicago Bilgin, Burhan, ve Çetin Camcı. “Timelike V-Bertrand Curves in Minkowski 3-Space $E_{1}^{3}$”. Journal of New Theory, sy. 38 (Mart 2022): 14-24. https://doi.org/10.53570/jnt.1051013.
EndNote Bilgin B, Camcı Ç (01 Mart 2022) Timelike V-Bertrand Curves in Minkowski 3-Space $E_{1}^{3}$. Journal of New Theory 38 14–24.
IEEE B. Bilgin ve Ç. Camcı, “Timelike V-Bertrand Curves in Minkowski 3-Space $E_{1}^{3}$”, JNT, sy. 38, ss. 14–24, Mart 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 (Mart 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 ve Çetin Camcı. “Timelike V-Bertrand Curves in Minkowski 3-Space $E_{1}^{3}$”. Journal of New Theory, sy. 38, 2022, ss. 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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