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

Burhan Bilgin; Çetin Camcı

doi:10.53570/jnt.1051013

EN

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

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.
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Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Authors

Burhan Bilgin ^*
0000-0002-3181-2031
Türkiye

Çetin Camcı
0000-0002-0122-559X
Türkiye

Publication Date

March 31, 2022

Submission Date

December 30, 2021

Acceptance Date

March 22, 2022

Published in Issue

Year 2022 Number: 38

DOI

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

IZ

https://izlik.org/JA85ZK56BB

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

1.Bilgin B, Camcı Ç. Timelike V-Bertrand Curves in Minkowski 3-Space $E_{1}^{3}$. JNT. 2022;(38):14-24. doi:10.53570/jnt.1051013

Chicago

Bilgin, Burhan, and Çetin Camcı. 2022. “Timelike V-Bertrand Curves in Minkowski 3-Space $E_{1}^{3}$”. Journal of New Theory, nos. 38: 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

[1]B. Bilgin and Ç. Camcı, “Timelike V-Bertrand Curves in Minkowski 3-Space $E_{1}^{3}$”, JNT, no. 38, pp. 14–24, Mar. 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 1, 2022): 14-24. https://doi.org/10.53570/jnt.1051013.

JAMA

1.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, Mar. 2022, pp. 14-24, doi:10.53570/jnt.1051013.

Vancouver

1.Burhan Bilgin, Çetin Camcı. Timelike V-Bertrand Curves in Minkowski 3-Space $E_{1}^{3}$. JNT. 2022 Mar. 1;(38):14-2. doi:10.53570/jnt.1051013