Research Article
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Year 2024, Volume: 17 Issue: 1, 252 - 258, 23.04.2024
https://doi.org/10.36890/iejg.1438073

Abstract

Project Number

2-15-2014

References

  • [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] Bertrand, J.M.: M’emoire sur la th’eorie des courbes a’ double courbure. Comptes Rendus. 15 (1), 332-350 (1850).
  • [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] 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] 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
  • [6] Deshmukh S., Chen B.-Y., Alghanemi A.: Natural mates of Frenet curves in Euclidean 3-space. Turk. J. Math. 42, 2826–2840 (2018).
  • [7] Deshmukh, S., Chen B.-Y., Turki N.B.: A differential equations for Frenet curves in Euclidean 3-space and its applications. Rom. J. Math. Comput. Sci. 8, 1-6 (2018).
  • [8] Menninger, T.: Characterization of the slant helix as successor curve of the general helix. Int. Electron. J. Geom. 7, 84-91 (2014).

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

Year 2024, Volume: 17 Issue: 1, 252 - 258, 23.04.2024
https://doi.org/10.36890/iejg.1438073

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.

Ethical Statement

This is joint work with Alex and has not been submitted anywhere else.

Supporting Institution

Andrews University

Project Number

2-15-2014

Thanks

Thank you for this exceptional opportunity!

References

  • [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] Bertrand, J.M.: M’emoire sur la th’eorie des courbes a’ double courbure. Comptes Rendus. 15 (1), 332-350 (1850).
  • [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] 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] 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
  • [6] Deshmukh S., Chen B.-Y., Alghanemi A.: Natural mates of Frenet curves in Euclidean 3-space. Turk. J. Math. 42, 2826–2840 (2018).
  • [7] Deshmukh, S., Chen B.-Y., Turki N.B.: A differential equations for Frenet curves in Euclidean 3-space and its applications. Rom. J. Math. Comput. Sci. 8, 1-6 (2018).
  • [8] Menninger, T.: Characterization of the slant helix as successor curve of the general helix. Int. Electron. J. Geom. 7, 84-91 (2014).
There are 8 citations in total.

Details

Primary Language English
Subjects Algebraic and Differential Geometry
Journal Section Research Article
Authors

Alexander Navarro 0000-0003-3545-1891

Yun Myung Oh 0000-0002-6526-8863

Project Number 2-15-2014
Early Pub Date April 12, 2024
Publication Date April 23, 2024
Submission Date February 16, 2024
Acceptance Date April 6, 2024
Published in Issue Year 2024 Volume: 17 Issue: 1

Cite

APA Navarro, A., & Oh, Y. M. (2024). Extending Natural Mates in Euclidean 3-space and Applications to Bertrand Pairs. International Electronic Journal of Geometry, 17(1), 252-258. https://doi.org/10.36890/iejg.1438073
AMA Navarro A, Oh YM. Extending Natural Mates in Euclidean 3-space and Applications to Bertrand Pairs. Int. Electron. J. Geom. April 2024;17(1):252-258. doi:10.36890/iejg.1438073
Chicago Navarro, Alexander, and Yun Myung Oh. “Extending Natural Mates in Euclidean 3-Space and Applications to Bertrand Pairs”. International Electronic Journal of Geometry 17, no. 1 (April 2024): 252-58. https://doi.org/10.36890/iejg.1438073.
EndNote Navarro A, Oh YM (April 1, 2024) Extending Natural Mates in Euclidean 3-space and Applications to Bertrand Pairs. International Electronic Journal of Geometry 17 1 252–258.
IEEE A. Navarro and Y. M. Oh, “Extending Natural Mates in Euclidean 3-space and Applications to Bertrand Pairs”, Int. Electron. J. Geom., vol. 17, no. 1, pp. 252–258, 2024, doi: 10.36890/iejg.1438073.
ISNAD Navarro, Alexander - Oh, Yun Myung. “Extending Natural Mates in Euclidean 3-Space and Applications to Bertrand Pairs”. International Electronic Journal of Geometry 17/1 (April 2024), 252-258. https://doi.org/10.36890/iejg.1438073.
JAMA Navarro A, Oh YM. Extending Natural Mates in Euclidean 3-space and Applications to Bertrand Pairs. Int. Electron. J. Geom. 2024;17:252–258.
MLA Navarro, Alexander and Yun Myung Oh. “Extending Natural Mates in Euclidean 3-Space and Applications to Bertrand Pairs”. International Electronic Journal of Geometry, vol. 17, no. 1, 2024, pp. 252-8, doi:10.36890/iejg.1438073.
Vancouver Navarro A, Oh YM. Extending Natural Mates in Euclidean 3-space and Applications to Bertrand Pairs. Int. Electron. J. Geom. 2024;17(1):252-8.