New Parametrization of Bertrand Partner D-curves in $\mathbb{E}^{3}$-Reference-Cited by-同舟云学术

New Parametrization of Bertrand Partner D-curves in $\mathbb{E}^{3}$

Published:2024-04-19 Issue: Volume:42 Page:1-11
ISSN:2175-1188
Container-title:Boletim da Sociedade Paranaense de Matemática
language:
Short-container-title:B Soc Paran Mat

Author:

Tamta Stuti^ORCID,Gupta Ram Shankar^ORCID

Abstract

We define and study a new parametrization of a Bertrand partner D-curve \{$\alpha$,$\alpha^{*}$\} in Euclidean 3-space by not taking Darboux frame element $g^{*}$ of Bertrand partner D-curve $\alpha^{*}$ parallel to $\overrightarrow{\alpha \alpha^{*}}$. We obtain a necessary and sufficient condition for a curve to be such type of Bertrand D-curves. Also, we obtain a characterization of a new parametrization of asymptotic Bertrand D-curves and provide an example.

Funder

University Grants Commission

Publisher

Sociedade Paranaense de Matemática

Reference13 articles.

1. Balgetir, H., Bektas, M., Ergut, M., Bertrand curve for non-null curves in 3-dimensional Lorentzian space, Hadronic J. 27(2), 229-236 (2004).

2. Balgetir, H., Bektas and Inoguchi, J., Null Bertrand curves in Minkowski 3-space and their characterizations, Note Mat. 23(1) 7-13, (2004).

3. Bektas, O. and Yuce, S., Special Involute-Evolute Partner D-Curves in E 3, Eur. J. Pure Appl. Math., 6(1), 20-29 (2013).

4. Bertrand, J. M., Memoire sur la theorie des courbes a double courbure, Comptes Rendus, 15, 332-350 (1850).

5. B. O. Neill, Semi-Riemannian Geometry, Academic press, New York, 1983.

Cited by 1 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Spherical Indicatrix of a New Approach to Bertrand Curves in Euclidean 3-space;KYUNGPOOK MATH J;2023