Research Article
Year 2022,
Volume: 51 Issue: 3, 632 - 645, 01.06.2022
Abstract
References
- [1] A.T. Ali, Position vectors of curves in the Galilean space $G_{3}$, Mat. Vesnik, 64, 200- 210, 2012.
- [2] F. Almaz and M.A. Külahcı, Some characterizations on the special tubular surfaces in Galilean space, Prespacetime Journal, 11 (7), 2020.
- [3] F. Almaz and M.A. Külahcı, A different interpretation on magnetic surfaces generated by special magnetic curve in $ Q^{2} \subset E_{1}^{3} $, Adıyaman University Journal of Science, 10 (12), 2020.
- [4] F. Almaz and M.A. Külahcı, The notes on rotational surfaces in Galilean space, Int. J. Geom. Methods Mod. Phys. 18 (2), 2021.
- [5] F. Almaz and M.A. Külahcı, A survey on tube surfaces in Galilean 3-space, Journal of Polytechnic, 2021, https://doi.org/10.2339/politeknik.747869
- [6] F. Almaz and M.A. Külahcı, The geodesics on special tubular surfaces generated by Darboux frame in G3, 18th International Geometry Symposium, 2021.
- [7] A.V. Aminova, Pseudo-Riemannian manifolds with common geodesics, Russian Math. Surveys, 48, 105-160, 1993.
- [8] M. Dede, Tubular surfaces in Galilean space, Math. Commun. 18(1), 209-217, 2013.
- [9] M.K. Karacan and Y. Yayli, On the geodesics of tubular surfaces in Minkowski 3−space, Bull. Malays. Math. Sci. Soc. 31 (1), 1-10, 2008.
- [10] E. Kasap and F.T. Akyildiz, Surfaces with a common geodesic in Minkowski 3−space, App. Math. Comp. 117 (1), 260-270, 2006.
- [11] Y.H. Kim and D.M. Yoon, On non-developable ruled surface in Lorentz Minkowski 3-spaces, Taiwanese J. Math. 11 (1), 197-214, 2007.
- [12] W. Kuhnel, Differential Geometry Curves-Surfaces and Manifolds, Second Edition, Amer. Math. Soc., Providence, RI, 2006.
- [13] Z. Milin-Šipuš and B. Divjak, Surfaces of Constant Curvature in the Pseudo-Galilean Space, Int. J. Math. Math. Sci. 1-28, 2012.
- [14] A. Pressley, Elementary Differential Geometry, Second edition, Springer-Verlag London Limited, 2010.
- [15] O. Röschel, Die Geometrie Des Galileischen Raumes, Forschungszentrum Graz, Mathematisch-Statistische Sektion, Graz, 1985.
- [16] O. Röschel, Die Geometrie Des Galileischen Raumes, Bericht Der Mathematisch Statistischen Sektion in Der Forschungs-Gesellschaft Joanneum, Bericht Nr. 256, Habilitationsschrift, Leoben, 1984.
- [17] A. Saad and R.J. Low, A generalized Clairaut’s theorem in Minkowski space, J. Geom. and Symmetry Phys. 35, 103-111, 2014.
- [18] T. Şahin, Intrinsic equations for a generalized relaxed elastic line on an oriented surface in the Galilean space, Acta Math. Sci. 33 (3), 701-711, 2013.
- [19] D.W. Yoon, Surfaces of revolution in the three dimensional pseudo-Galilean space, Glasnik Matematicki, 48 (68), 415-428, 2013.
Year 2022,
Volume: 51 Issue: 3, 632 - 645, 01.06.2022
Abstract
In this paper, we study the special tube surfaces generated by rectifying curves with respect to the Darboux frame in terms of the geodesic curvature, the normal curvature and the geodesic torsion in Galilean 3-space. During this study we establish some definite results of geodesics on specific tube surfaces with the help of Clairaut’s theorem in detail and we compute the Gaussian curvature and the mean curvature of the special tube surfaces with respect to the Darboux frame. After that, considering the geodesic conditions and the curvatures of the special tube surface, we give some theorems for the rectifying curves with $v$-parameter (and $w$-parameter) being a geodesic curve and an asymptotic curve, respectively.
References
- [1] A.T. Ali, Position vectors of curves in the Galilean space $G_{3}$, Mat. Vesnik, 64, 200- 210, 2012.
- [2] F. Almaz and M.A. Külahcı, Some characterizations on the special tubular surfaces in Galilean space, Prespacetime Journal, 11 (7), 2020.
- [3] F. Almaz and M.A. Külahcı, A different interpretation on magnetic surfaces generated by special magnetic curve in $ Q^{2} \subset E_{1}^{3} $, Adıyaman University Journal of Science, 10 (12), 2020.
- [4] F. Almaz and M.A. Külahcı, The notes on rotational surfaces in Galilean space, Int. J. Geom. Methods Mod. Phys. 18 (2), 2021.
- [5] F. Almaz and M.A. Külahcı, A survey on tube surfaces in Galilean 3-space, Journal of Polytechnic, 2021, https://doi.org/10.2339/politeknik.747869
- [6] F. Almaz and M.A. Külahcı, The geodesics on special tubular surfaces generated by Darboux frame in G3, 18th International Geometry Symposium, 2021.
- [7] A.V. Aminova, Pseudo-Riemannian manifolds with common geodesics, Russian Math. Surveys, 48, 105-160, 1993.
- [8] M. Dede, Tubular surfaces in Galilean space, Math. Commun. 18(1), 209-217, 2013.
- [9] M.K. Karacan and Y. Yayli, On the geodesics of tubular surfaces in Minkowski 3−space, Bull. Malays. Math. Sci. Soc. 31 (1), 1-10, 2008.
- [10] E. Kasap and F.T. Akyildiz, Surfaces with a common geodesic in Minkowski 3−space, App. Math. Comp. 117 (1), 260-270, 2006.
- [11] Y.H. Kim and D.M. Yoon, On non-developable ruled surface in Lorentz Minkowski 3-spaces, Taiwanese J. Math. 11 (1), 197-214, 2007.
- [12] W. Kuhnel, Differential Geometry Curves-Surfaces and Manifolds, Second Edition, Amer. Math. Soc., Providence, RI, 2006.
- [13] Z. Milin-Šipuš and B. Divjak, Surfaces of Constant Curvature in the Pseudo-Galilean Space, Int. J. Math. Math. Sci. 1-28, 2012.
- [14] A. Pressley, Elementary Differential Geometry, Second edition, Springer-Verlag London Limited, 2010.
- [15] O. Röschel, Die Geometrie Des Galileischen Raumes, Forschungszentrum Graz, Mathematisch-Statistische Sektion, Graz, 1985.
- [16] O. Röschel, Die Geometrie Des Galileischen Raumes, Bericht Der Mathematisch Statistischen Sektion in Der Forschungs-Gesellschaft Joanneum, Bericht Nr. 256, Habilitationsschrift, Leoben, 1984.
- [17] A. Saad and R.J. Low, A generalized Clairaut’s theorem in Minkowski space, J. Geom. and Symmetry Phys. 35, 103-111, 2014.
- [18] T. Şahin, Intrinsic equations for a generalized relaxed elastic line on an oriented surface in the Galilean space, Acta Math. Sci. 33 (3), 701-711, 2013.
- [19] D.W. Yoon, Surfaces of revolution in the three dimensional pseudo-Galilean space, Glasnik Matematicki, 48 (68), 415-428, 2013.
There are 19 citations in total.
Details
| Primary Language | English |
|---|---|
| Subjects | Mathematical Sciences |
| Journal Section | Mathematics |
| Authors | |
| Publication Date | June 1, 2022 |
| Published in Issue | Year 2022 Volume: 51 Issue: 3 |