Extending Natural Mates in Euclidean 3-space and Applications to Bertrand Pairs-Reference-Cited by-同舟云学术

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Extending Natural Mates in Euclidean 3-space and Applications to Bertrand Pairs

Published:2024-04-23 Issue:1 Volume:17 Page:252-258
ISSN:1307-5624
Container-title:International Electronic Journal of Geometry
language:
Short-container-title:

Author:

Navarro Alexander¹^ORCID,Oh Yun Myung¹^ORCID

Affiliation:

1. Andrews University

Abstract

In Euclidean 3-space, a family of curves, the co-successor, is motivated and then introduced in relation to the natural mate. A complete characterization of co-successors is proved, followed by an application of the co-successor towards describing Bertrand curves and their mates.

Funder

Andrews University

Publisher

International Electronic Journal of Geometry, Person (Kazim ILARSLAN)

Reference8 articles.

1. [1] Alghanemi, A., Khan, M.A.: Position Vectors of the Natural Mate and Conjugate of a Space Curve. Adv. Math. Phys., 1-5 (2023). https://doi.org/10.1155/2023/7565988

2. [2] Bertrand, J.M.: M’emoire sur la th’eorie des courbes a’ double courbure. Comptes Rendus. 15 (1), 332-350 (1850).

3. [3] Camci, Ç., Chen, B.-Y., ˙Ilarslan, K. et al.: Sequential natural mates of Frenet curves in Euclidean 3-space. J. Geom. 112, 46 (2021). https://doi.org/10.1007/s00022-021-00610-6

4. [4] Chen, B.-Y.: When does the position vector of a space curve always lie in its rectifying plane?. Amer. Math. Monthly. 110, 147-152 (2003).

5. [5] Choi, J. H., Kim, Y. H.: Associated curves of a Frenet curve and their applications. Appl. Math. Comput. 218 (18), 9116-9124 (2012). https://doi.org/10.1016/j.amc.2012.02.064

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