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Year 2024, Volume: 42 Issue: 1, 37 - 41, 27.02.2024

Abstract

References

  • REFERENCES
  • [1] Tzitzeica G. Sur Certaines Courbes Gouches. Ann De I’Ec Normale Sup. 1911;28:9–32. [CrossRef]
  • [2] Agnew AF, Bobe A, Boskoff WG, Suceava BD. Tzitzeica curves and surfaces. Math J 2010;12:1–18. [CrossRef]
  • [3] Karacan MK, Bükçü B. On the elliptic cylindrical Tzitzeica curves in Minkowski 3-space. Sci Manga 2009:44–48.
  • [4] Crasmareanu M. Cylindrical Tzitzeica curves implies forced harmonic oscillators. Balkan J Geom Appl 2002;7:37–42.
  • [5] Constantinescu O, Crasmareanu M. A new Tzitzeica hypersurface and cubic Finslerian metrics of Berwald type. Balkan J Geom Appl 2011;16:27–34.
  • [6] Bobe A, Boskoff WG, Ciuca MG. Tzitzeica-Type centro-affine invariants in Minkowski spaces. An St Univ Ovidius Constanta 2012;20:27–34. [CrossRef]
  • [7] Bila N. Symmetry reductions for the Tzitzeica curve equation. Math and Comp Sci 2012;16.
  • [8] Bayram B, Tunç E, Arslan K, Öztürk G. On Tzitzeica curves in Euclidean 3-space. Facta Univ Ser Math Inform 2018;33:409–416. [CrossRef]
  • [9] Özen KE, Tosun M. Characterization of Tzitzeica curves using positional adapted frame. 2022;10:260268.
  • [10] Eren K, Ersoy S. Characterizations of Tzitzeica curves using Bishop frames. Math Meth Appl Sci 2021;1–14. [CrossRef]
  • [11] O'Neill B. Elementary Differential Geometry. New York: Academic Press Inc.; 1966. [CrossRef]
  • [12] Dede M. A new representation of tubular surfaces. Houston J Math 2019;45:707–720.

Characterizations of tzitzeica curves using FLC frame

Year 2024, Volume: 42 Issue: 1, 37 - 41, 27.02.2024

Abstract

In this study, we investigate the condition that a given polynomial curve with respect to the Frenet like curve (Flc) frame is a Tzitzeica curve. We also show that any planar polynomial curve cannot be a Tzitzeica curve. Finally, the condition to be the Tzitzeica curve for each of the spherical indicatrix curves defined according to the Flc frame is expressed, separately.

References

  • REFERENCES
  • [1] Tzitzeica G. Sur Certaines Courbes Gouches. Ann De I’Ec Normale Sup. 1911;28:9–32. [CrossRef]
  • [2] Agnew AF, Bobe A, Boskoff WG, Suceava BD. Tzitzeica curves and surfaces. Math J 2010;12:1–18. [CrossRef]
  • [3] Karacan MK, Bükçü B. On the elliptic cylindrical Tzitzeica curves in Minkowski 3-space. Sci Manga 2009:44–48.
  • [4] Crasmareanu M. Cylindrical Tzitzeica curves implies forced harmonic oscillators. Balkan J Geom Appl 2002;7:37–42.
  • [5] Constantinescu O, Crasmareanu M. A new Tzitzeica hypersurface and cubic Finslerian metrics of Berwald type. Balkan J Geom Appl 2011;16:27–34.
  • [6] Bobe A, Boskoff WG, Ciuca MG. Tzitzeica-Type centro-affine invariants in Minkowski spaces. An St Univ Ovidius Constanta 2012;20:27–34. [CrossRef]
  • [7] Bila N. Symmetry reductions for the Tzitzeica curve equation. Math and Comp Sci 2012;16.
  • [8] Bayram B, Tunç E, Arslan K, Öztürk G. On Tzitzeica curves in Euclidean 3-space. Facta Univ Ser Math Inform 2018;33:409–416. [CrossRef]
  • [9] Özen KE, Tosun M. Characterization of Tzitzeica curves using positional adapted frame. 2022;10:260268.
  • [10] Eren K, Ersoy S. Characterizations of Tzitzeica curves using Bishop frames. Math Meth Appl Sci 2021;1–14. [CrossRef]
  • [11] O'Neill B. Elementary Differential Geometry. New York: Academic Press Inc.; 1966. [CrossRef]
  • [12] Dede M. A new representation of tubular surfaces. Houston J Math 2019;45:707–720.
There are 13 citations in total.

Details

Primary Language English
Subjects Biochemistry and Cell Biology (Other)
Journal Section Research Articles
Authors

Süleyman Şenyurt 0000-0003-1097-5541

Kemal Eren 0000-0001-5273-7897

Kebire Hilal Ayvacı 0000-0002-5114-5475

Publication Date February 27, 2024
Submission Date January 7, 2022
Published in Issue Year 2024 Volume: 42 Issue: 1

Cite

Vancouver Şenyurt S, Eren K, Ayvacı KH. Characterizations of tzitzeica curves using FLC frame. SIGMA. 2024;42(1):37-41.

IMPORTANT NOTE: JOURNAL SUBMISSION LINK https://eds.yildiz.edu.tr/sigma/