Generalized Bertrand and Mannheim Curves in 3D Lie Groups-Reference-Cited by-同舟云学术

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Generalized Bertrand and Mannheim Curves in 3D Lie Groups

Published:2022-08-10 Issue: Volume: Page:
ISSN:2645-8845
Container-title:Fundamental Journal of Mathematics and Applications
language:en
Short-container-title:FUJMA

Author:

OKUYUCU Osman Zeki¹,DOĞAN YAZICI Bahar¹

Affiliation:

1. BILECIK SEYH EDEBALI UNIVERSITY

Abstract

In this paper, we give a new approach for Bertrand and Mannheim curves in 3D Lie groups with bi-invariant metric. By the this way, some conditions including the known results have been given for a curve to be Bertrand or Mannheim curve in 3D Euclidean space and in 3D Lie groups.

Publisher

Fundamental Journal of Mathematics and Applications

Subject

Materials Chemistry

Reference12 articles.

1. Lancret, M. A. Memoire sur les courbes ´ a double courbure, M ` emoires pr ´ esent ´ es´ a l’Institut1, 1806, pp. 416–454. `

2. S. Izumiya, N. Tkeuchi, New special curves and developable surfaces, Turk. J. Math., 28 (2004), 153-163.

3. J. M. Bertrand, M´emoire sur la th´eorie des courbes ´a double courbure, Comptes Rendus, vol.36, 1850.

4. H., Liu, F., Wang, Mannheim partner curves in 3-space, J. Geom., 88 (2008) 120–126.

5. C¸ . Camci, A. Uc¸um, K. ˙Ilarslan, A new approach to Bertrand curves in Euclidean 3-space, J. Geom., 111, 49 (2020).

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1. Mannheim partner curves in the special linear group;International Journal of Physical Sciences;2023-03-31

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