Araştırma Makalesi
Yıl 2024,
Cilt: 16 Sayı: 2, 498 - 506, 31.12.2024
Öz
This paper investigates position vectors of arbitrary curves in isotropic 3-space (denoted by I^3). We first establish the relationship between a curve’s position vector and the Frenet frame. Then, we derive a natural representation of any curve’s position vector using curvature and torsion. Furthermore, we define various curves within isotropic space, including straight lines, plane curves, helices, general helices, Salkowski curves, and anti-Salkowski curves. Finally, graphical illustrations accompany illustrative examples to elucidate the discussed concepts.
Anahtar Kelimeler
Kaynakça
- Ali, A.T., Position vectors of spacelike general helices in Minkowski 3-space, Nonlin. Anal. Theory Meth. Appl., 73(2010), 1118–1126.
- Ali, A.T., Position vectors of slant helices in Euclidean 3-space, Journal of the Egyptian Mathematical Society, 20(1)(2012), 1–6.
- Ali, A.T., Position vectors of curves in the Galilean space G3, Matemati˘cki Vesnik, 64(3)(2012), 200–210.
- Aydın, M.E., A generalization of translation surfaces with constant curvature in the isotropic space, J. Geom., 107(2016), 603–615.
- Brauner, H., Geometrie des Zweifach Isotropen Raumes I, J. Reine Angew. Math., 224(1966), 118–146.
- Erjavec, Z., Divjak, B., Horvat, D. The general solutions of Frenet’s system in the equiform geometry of the Galilean, pseudo-Galilean , simple isotropic and double isotropic space, International Mathematical Forum, 6(17)(2011), 837–856.
- Güzelkardeşler, G., Şahiner, B., An alternative method for determination of the position vector of a slant helix, Journal of New Theory, 44(2023), 97–105.
- Izumiya, S., Takeuchi,N., New special curves and developable surfaces, Turk. J. Math., 28(2004), 531–537.
- Kızıltuğ, S., Kaya, S., Tarakçı, Ö ., The slant helices according to type-2 bishop frame in Euclidean 3-space, International Journal of Pure and Applied Mathematics, 85(2)(2013), 211–222.
- Molnar, E., The projective interpretation of the eight 3-dimensional homogeneous geometries, Beitr. Algebra Geom., 38(1997), 261–288.
- Monterde, J., Salkowski curves revisted: A family of curves with constant curvature and non-constant torsion, Comput. Aided Geomet. Design, 26(2009), 271–278.
- Osman Öğrenmiş, A., Külahçı, M., Bektaş, M., A Survey for some special curves in isotropic space,Physical Review Research International, 3(4)(2013), 321–329.
- Özyurt, G., Position Vectors and Characterization of Curves in the Isotropic Space, Master Thesis, Institute of Sciences, Amasya University, Amasya, 2021.
- Pavkovic, B.J., Kamenarovic, I., The general solution of the Frenet’s system in the doubly isotropic space I(2) 3 , Rad JAZU, 428(1987), 17–24.
- Pavkovi´c, B.J., Kamenarovi´c, I., The equiform differential geometry of curves in the Galilean space, Glasnik Matematik˘ci, 22(42)(1987), 449–457.
- Pavkovi´c, B.J., The general solution of the Frenet system of differential equations for curves in the Galilean space G3, Rad HAZU Math., 450 (1990), 123–128.
- Sachs, H., Isotrope Geometrie des Raumes, Vieweg, Braunschweig/ Wiesbaden, 1990.
- Salkowski, E., Zur transformation von raumkurven, Math. Ann., 66(1909), 517–557.
- Şahin, T., Ceylan Dirişen, B., Position vectors of curves with respect to Darboux frame in the Galilean space G3, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., 68(2)(2019), 2079–2093.
Yıl 2024,
Cilt: 16 Sayı: 2, 498 - 506, 31.12.2024
Öz
Kaynakça
- Ali, A.T., Position vectors of spacelike general helices in Minkowski 3-space, Nonlin. Anal. Theory Meth. Appl., 73(2010), 1118–1126.
- Ali, A.T., Position vectors of slant helices in Euclidean 3-space, Journal of the Egyptian Mathematical Society, 20(1)(2012), 1–6.
- Ali, A.T., Position vectors of curves in the Galilean space G3, Matemati˘cki Vesnik, 64(3)(2012), 200–210.
- Aydın, M.E., A generalization of translation surfaces with constant curvature in the isotropic space, J. Geom., 107(2016), 603–615.
- Brauner, H., Geometrie des Zweifach Isotropen Raumes I, J. Reine Angew. Math., 224(1966), 118–146.
- Erjavec, Z., Divjak, B., Horvat, D. The general solutions of Frenet’s system in the equiform geometry of the Galilean, pseudo-Galilean , simple isotropic and double isotropic space, International Mathematical Forum, 6(17)(2011), 837–856.
- Güzelkardeşler, G., Şahiner, B., An alternative method for determination of the position vector of a slant helix, Journal of New Theory, 44(2023), 97–105.
- Izumiya, S., Takeuchi,N., New special curves and developable surfaces, Turk. J. Math., 28(2004), 531–537.
- Kızıltuğ, S., Kaya, S., Tarakçı, Ö ., The slant helices according to type-2 bishop frame in Euclidean 3-space, International Journal of Pure and Applied Mathematics, 85(2)(2013), 211–222.
- Molnar, E., The projective interpretation of the eight 3-dimensional homogeneous geometries, Beitr. Algebra Geom., 38(1997), 261–288.
- Monterde, J., Salkowski curves revisted: A family of curves with constant curvature and non-constant torsion, Comput. Aided Geomet. Design, 26(2009), 271–278.
- Osman Öğrenmiş, A., Külahçı, M., Bektaş, M., A Survey for some special curves in isotropic space,Physical Review Research International, 3(4)(2013), 321–329.
- Özyurt, G., Position Vectors and Characterization of Curves in the Isotropic Space, Master Thesis, Institute of Sciences, Amasya University, Amasya, 2021.
- Pavkovic, B.J., Kamenarovic, I., The general solution of the Frenet’s system in the doubly isotropic space I(2) 3 , Rad JAZU, 428(1987), 17–24.
- Pavkovi´c, B.J., Kamenarovi´c, I., The equiform differential geometry of curves in the Galilean space, Glasnik Matematik˘ci, 22(42)(1987), 449–457.
- Pavkovi´c, B.J., The general solution of the Frenet system of differential equations for curves in the Galilean space G3, Rad HAZU Math., 450 (1990), 123–128.
- Sachs, H., Isotrope Geometrie des Raumes, Vieweg, Braunschweig/ Wiesbaden, 1990.
- Salkowski, E., Zur transformation von raumkurven, Math. Ann., 66(1909), 517–557.
- Şahin, T., Ceylan Dirişen, B., Position vectors of curves with respect to Darboux frame in the Galilean space G3, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., 68(2)(2019), 2079–2093.
Toplam 19 adet kaynakça vardır.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Cebirsel ve Diferansiyel Geometri |
| Bölüm | Makaleler |
| Yazarlar | |
| Yayımlanma Tarihi | 31 Aralık 2024 |
| Gönderilme Tarihi | 26 Mayıs 2024 |
| Kabul Tarihi | 15 Ekim 2024 |
| Yayımlandığı Sayı | Yıl 2024 Cilt: 16 Sayı: 2 |