Research Article

According to The Frenet Frame Spherical Indicators and Results on E^3

Volume: 6 Number: 2 July 30, 2025
EN

According to The Frenet Frame Spherical Indicators and Results on E^3

Abstract

In this study, we showed that the spherical indicator curve frames can correspond to a Bishop frame according to the Serret-Frenet frame of a regular curve.

Keywords

Supporting Institution

The research was supported by Harran University Scientific Research Projects Unit as project number 23056.

Project Number

23056

Ethical Statement

The authors declare that the materials and methods used in their study do not require ethical committee and/or legal special permission.

References

  1. Akgün M.A., Frenet curves in 3-dimensıonal contact Lorentzian manifolds, Facta Universitatis, Series: Mathematics and Informatics, 37(1), 67-76, 2022.
  2. Ateş F., Kocakuşaklı E., Gök İ., Yaylı Y., A study of the tubular surfaces constructed by the spherical indicatrices in Euclidean 3-spaces, Turkish Journal of Mathematics, 42(4), 1711-1725, 2018.
  3. Bilici M., The Curvatures and the Natural Lifts of the Spherical Indicator Curves of the Involute- Evolute Curve, Master Thesis, Ondokuz Mayıs University, Samsun, Türkiye, 1999.
  4. Bishop L.R., There is more than one way to frame a curve, The American Mathematical Monthly, 82(3), 246-251, 1975.
  5. Çapın R., Spherical Indicator Curves in Minkowski Space, Master Thesis, Gaziantep University, Gaziantep, Türkiye, 2016.
  6. Erkan E., Yüce S., Serret-Frenet frame and curvatures of B´ezier curves, Mathematics, 6(12), 321, 2018.
  7. Frenet J.F., Sur les Fonctions Qui Servent `a D´eterminer L’attraction des Sph´ero¨ıdes Quelconques, Doctoral Thesis, Chauvin A., 1847.
  8. Kula L., Yaylı Y., On slant helix and its spherical indicatrix, Applied Mathematics and Computation, 169(1), 600-607, 2005.

Details

Primary Language

English

Subjects

Algebraic and Differential Geometry

Journal Section

Research Article

Publication Date

July 30, 2025

Submission Date

November 5, 2024

Acceptance Date

April 2, 2025

Published in Issue

Year 2025 Volume: 6 Number: 2

APA
Yıldırım, A., & Toktimur, A. (2025). According to The Frenet Frame Spherical Indicators and Results on E^3. Fundamentals of Contemporary Mathematical Sciences, 6(2), 123-138. https://doi.org/10.54974/fcmathsci.1579741
AMA
1.Yıldırım A, Toktimur A. According to The Frenet Frame Spherical Indicators and Results on E^3. FCMS. 2025;6(2):123-138. doi:10.54974/fcmathsci.1579741
Chicago
Yıldırım, Abdullah, and Ali Toktimur. 2025. “According to The Frenet Frame Spherical Indicators and Results on E^3”. Fundamentals of Contemporary Mathematical Sciences 6 (2): 123-38. https://doi.org/10.54974/fcmathsci.1579741.
EndNote
Yıldırım A, Toktimur A (July 1, 2025) According to The Frenet Frame Spherical Indicators and Results on E^3. Fundamentals of Contemporary Mathematical Sciences 6 2 123–138.
IEEE
[1]A. Yıldırım and A. Toktimur, “According to The Frenet Frame Spherical Indicators and Results on E^3”, FCMS, vol. 6, no. 2, pp. 123–138, July 2025, doi: 10.54974/fcmathsci.1579741.
ISNAD
Yıldırım, Abdullah - Toktimur, Ali. “According to The Frenet Frame Spherical Indicators and Results on E^3”. Fundamentals of Contemporary Mathematical Sciences 6/2 (July 1, 2025): 123-138. https://doi.org/10.54974/fcmathsci.1579741.
JAMA
1.Yıldırım A, Toktimur A. According to The Frenet Frame Spherical Indicators and Results on E^3. FCMS. 2025;6:123–138.
MLA
Yıldırım, Abdullah, and Ali Toktimur. “According to The Frenet Frame Spherical Indicators and Results on E^3”. Fundamentals of Contemporary Mathematical Sciences, vol. 6, no. 2, July 2025, pp. 123-38, doi:10.54974/fcmathsci.1579741.
Vancouver
1.Abdullah Yıldırım, Ali Toktimur. According to The Frenet Frame Spherical Indicators and Results on E^3. FCMS. 2025 Jul. 1;6(2):123-38. doi:10.54974/fcmathsci.1579741

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