Research Article
Year 2021,
Volume: 13 Issue: 2, 379 - 387, 31.12.2021
Abstract
References
- [1] Bishop, R.L., There is more than one way to Frame a curve, American Mathematical Monthly, 82(3)(1975), 246–251.
- [2] Capın, R., Minkowski Uzayında Küresel Gösterge Eğrileri, Yüksek Lisans Tezi, Gaziantep Üniversitesi Fen Bilimleri Enstitüsü, Gaziantep, 77p, 2016.
- [3] Dede, M., A new representation of tubular surfaces, Houston J. Math. 45(3)(2019), 707—720.
- [4] Farouki, R.T., Han, C.Y., Manni, C., Sestini, A., Characterization and construction of helical polynomial space curves, Journal of Computational and Applied Mathematics 162(2004), 365-–392.
- [5] Gökyeşil, D., Dual Uzayda Bazı Eğrilerin Dual Bishop Çatısına Göre Karakterizasyonları, Yüksek Lisans Tezi, Manisa Celal Bayar Üniversitesi Fen Bilimleri Enstitüsü , Manisa, 65p, 2018.
- [6] Hacısalihogğlu, H.H., Diferansiyel Geometri, Ankara Üniversitesi Fen Fakültesi, Ankara, 1993.
- [7] Kula, L., Yayli, Y. On slant helix and its spherical indicatrix, Appl. Math. Comput., 169(1)(2005), 600–607.
- [8] Larson, R., Elemantary Linear Algebra, The Pennsylvania State University, Boston, 2012.
- [9] O’Neill, B., Elementary Diferential Geometry. New York, Academic Press Inc., 1966.
- [10] Şenyurt, S., Natural lifts and the geodesic sprays for the spherical indicatrices of the Mannheim partner curves in E3, International Journal of the Physical Sciences, 7(16)(2012), 2414–2421.
- [11] Şenyurt, S., Özgüner, Z., Bertrand eğri çiftinin küresel göstergelerinin geodezik eğrilikleri ve tabii liftleri, Ordu Üniv. Bil. Tek. Derg., 3(2)(2013), 58–81.
- [12] Yılmaz, S., Özyılmaz, E., Turgut, M., New spherical indicatrices and their characterizations, An. Şt. Univ. Ovidius Constanta., 18(2)(2010), 337–354.
Year 2021,
Volume: 13 Issue: 2, 379 - 387, 31.12.2021
Abstract
In this study, the spherical indicatrices of Flc frame vectors were defined on unit sphere. The arc length parameters and the Frenet vectors of these indicatrix curves were calculated, as well. Last, we have provided the geodesic curvatures according to both Euclidean space $E^3$ and unit sphere $S^2$.
References
- [1] Bishop, R.L., There is more than one way to Frame a curve, American Mathematical Monthly, 82(3)(1975), 246–251.
- [2] Capın, R., Minkowski Uzayında Küresel Gösterge Eğrileri, Yüksek Lisans Tezi, Gaziantep Üniversitesi Fen Bilimleri Enstitüsü, Gaziantep, 77p, 2016.
- [3] Dede, M., A new representation of tubular surfaces, Houston J. Math. 45(3)(2019), 707—720.
- [4] Farouki, R.T., Han, C.Y., Manni, C., Sestini, A., Characterization and construction of helical polynomial space curves, Journal of Computational and Applied Mathematics 162(2004), 365-–392.
- [5] Gökyeşil, D., Dual Uzayda Bazı Eğrilerin Dual Bishop Çatısına Göre Karakterizasyonları, Yüksek Lisans Tezi, Manisa Celal Bayar Üniversitesi Fen Bilimleri Enstitüsü , Manisa, 65p, 2018.
- [6] Hacısalihogğlu, H.H., Diferansiyel Geometri, Ankara Üniversitesi Fen Fakültesi, Ankara, 1993.
- [7] Kula, L., Yayli, Y. On slant helix and its spherical indicatrix, Appl. Math. Comput., 169(1)(2005), 600–607.
- [8] Larson, R., Elemantary Linear Algebra, The Pennsylvania State University, Boston, 2012.
- [9] O’Neill, B., Elementary Diferential Geometry. New York, Academic Press Inc., 1966.
- [10] Şenyurt, S., Natural lifts and the geodesic sprays for the spherical indicatrices of the Mannheim partner curves in E3, International Journal of the Physical Sciences, 7(16)(2012), 2414–2421.
- [11] Şenyurt, S., Özgüner, Z., Bertrand eğri çiftinin küresel göstergelerinin geodezik eğrilikleri ve tabii liftleri, Ordu Üniv. Bil. Tek. Derg., 3(2)(2013), 58–81.
- [12] Yılmaz, S., Özyılmaz, E., Turgut, M., New spherical indicatrices and their characterizations, An. Şt. Univ. Ovidius Constanta., 18(2)(2010), 337–354.
There are 12 citations in total.
Details
| Primary Language | English |
|---|---|
| Subjects | Mathematical Sciences |
| Journal Section | Articles |
| Authors | |
| Publication Date | December 31, 2021 |
| Published in Issue | Year 2021 Volume: 13 Issue: 2 |