Research Article
Year 2025,
Volume: 6 Issue: 2, 123 - 138, 30.07.2025
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.
Ethical Statement
The authors declare that the materials and methods used in their study do not require ethical committee and/or legal special permission.
Supporting Institution
The research was supported by Harran University Scientific Research Projects Unit as project number 23056.
Project Number
23056
References
- Akgün M.A., Frenet curves in 3-dimensıonal contact Lorentzian manifolds, Facta Universitatis, Series: Mathematics and Informatics, 37(1), 67-76, 2022.
- 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.
- 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.
- Bishop L.R., There is more than one way to frame a curve, The American Mathematical Monthly, 82(3), 246-251, 1975.
- Çapın R., Spherical Indicator Curves in Minkowski Space, Master Thesis, Gaziantep University, Gaziantep, Türkiye, 2016.
- Erkan E., Yüce S., Serret-Frenet frame and curvatures of B´ezier curves, Mathematics, 6(12), 321, 2018.
- Frenet J.F., Sur les Fonctions Qui Servent `a D´eterminer L’attraction des Sph´ero¨ıdes Quelconques, Doctoral Thesis, Chauvin A., 1847.
- Kula L., Yaylı Y., On slant helix and its spherical indicatrix, Applied Mathematics and Computation, 169(1), 600-607, 2005.
- Şahin B., Diferansiyel Geometri, Palme Yayınevi, 2021.
- Şenyurt S., Çalışkan Ö.F., The natural lift curves and geodesic curvatures of the spherical indicatrices of the timelike bertrand curve couple, International Electronic Journal of Geometry, 6(2), 88-99, 2013.
- Şenyurt S., Demet S., Timelike-spacelike Mannheim pair curves spherical indicators geodesic curvatures and natural lifts, International Journal of Mathematical Combinatorics, 2, 32-54, 2015.
- Yıldırım A., On curves in 3-dimensional normal almost contact metric manifolds, International Journal of Geometric Methods in Modern Physics, 18(1), 2150004, 2021.
Year 2025,
Volume: 6 Issue: 2, 123 - 138, 30.07.2025
Abstract
Project Number
23056
References
- Akgün M.A., Frenet curves in 3-dimensıonal contact Lorentzian manifolds, Facta Universitatis, Series: Mathematics and Informatics, 37(1), 67-76, 2022.
- 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.
- 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.
- Bishop L.R., There is more than one way to frame a curve, The American Mathematical Monthly, 82(3), 246-251, 1975.
- Çapın R., Spherical Indicator Curves in Minkowski Space, Master Thesis, Gaziantep University, Gaziantep, Türkiye, 2016.
- Erkan E., Yüce S., Serret-Frenet frame and curvatures of B´ezier curves, Mathematics, 6(12), 321, 2018.
- Frenet J.F., Sur les Fonctions Qui Servent `a D´eterminer L’attraction des Sph´ero¨ıdes Quelconques, Doctoral Thesis, Chauvin A., 1847.
- Kula L., Yaylı Y., On slant helix and its spherical indicatrix, Applied Mathematics and Computation, 169(1), 600-607, 2005.
- Şahin B., Diferansiyel Geometri, Palme Yayınevi, 2021.
- Şenyurt S., Çalışkan Ö.F., The natural lift curves and geodesic curvatures of the spherical indicatrices of the timelike bertrand curve couple, International Electronic Journal of Geometry, 6(2), 88-99, 2013.
- Şenyurt S., Demet S., Timelike-spacelike Mannheim pair curves spherical indicators geodesic curvatures and natural lifts, International Journal of Mathematical Combinatorics, 2, 32-54, 2015.
- Yıldırım A., On curves in 3-dimensional normal almost contact metric manifolds, International Journal of Geometric Methods in Modern Physics, 18(1), 2150004, 2021.
There are 12 citations in total.
Details
| Primary Language | English |
|---|---|
| Subjects | Algebraic and Differential Geometry |
| Journal Section | Research Articles |
| Authors | |
| Project Number | 23056 |
| Publication Date | July 30, 2025 |
| Submission Date | November 5, 2024 |
| Acceptance Date | April 2, 2025 |
| Published in Issue | Year 2025 Volume: 6 Issue: 2 |
FCMS is licensed under the Creative Commons Attribution 4.0 International Public License.