A New Approach for Inextensible Flows of Curves in Pseudo-Galilean Space $G_{3}^{1}$

Yıl 2021, Cilt: 9 Sayı: 1, 19 - 23, 28.04.2021

Hülya Gün Bozok

Öz

In this paper, inextensible flows of a spacelike curve on a ruled surface of type I in 3-dimensional pseudo-Galilean space $G_{3}^{1}$ are researched. Firstly inextensible flows of these curves according to Darboux frame are determined then necessary and sufficient conditions for inextensible flows of the curves are expressed as a partial differential equation involving the curvature with this frame in $G_{3}^{1}$.

Anahtar Kelimeler

Inextensible flows, Darboux frame, pseudo-Galilean space

Kaynakça

• [1] H.S. Abdel-Aziz, Spinor Frenet and Darboux equations of spacelike curves in pseudo-Galilean geometry, Communications in Algebra, 45, (2017), 4321-4328.
• [2] M. Desbrun and M.P. Cani-Gascuel, Active implicit surface for animation, Proceedings of the Graphics Interface,Canada, (1998), 143-150.
• [3] B. Divjak, Curves in pseudo-Galilean geometry, Annales Univ. Sci. Budapest, 41, (1998), 117-128.
• [4] B. Divjak, Special curves on ruled surfaces in Galilean and pseudo-Galilean space, Acta Math. Hungar., 98, (2003), 203-215.
• [5] C. Ekici and M. Dede, On the Darboux vector of ruled surfaces in pseudo-Galilean space, Math. Comput. Appl., 16, (2011), 830-838.
• [6] M. Gage and R.S. Hamilton, The heat equation shrinking convex plane curves, J. Differential Geom., 23, (1986), 69-96.
• [7] M. Grayson, The heat equation shrinks embedded plane curves to round points, J. Differential Geom., 26, (1987), 285-314.
• [8] M. Kass, A. Witkin and D. Terzopoulos, Snakes: active contour models, Proc. 1st Int. Conference on Computer Vision, (1987), 259-268.
• [9] Z. Kucukarslan Yuzbasi and D.W. Yoon, Inextensible flows of curves on ligthlike surfaces, Mathematics, 6, (2018), 224.
• [10] D.Y. Kwon and F.C. Park, Evolution of inelastic plane curves, Appl. Math. Lett., 12,(1999), 115-119.
• [11] D.Y. Kwon, F.C. Park and D.P. Chi, Inextensible flows of curves and developable surfaces, Applied Mathematics Letters, 18, (2005), 1156-1162.
• [12] D. Latifi and A. Razavi, Inextensible flows of curves in Minkowskian Space, Adv. Studies Theor. Phys., 2, (2008), 761-768.
• [13] H.Q. Lu, J.S. Todhunter and T.W. Sze, Congruence conditions for nonplanar developable surfaces and their application to surface recognition, CVGIP,Image Underst., 56, (1993), 265-285.
• [14] A.O. Ogrenmis and M. Yeneroglu, Inextensible curves in the Galilean space, International Journal of the Physical Sciences, 5, (2010), 1424-1427.
• [15] H. Oztekin and H. Gun Bozok, Inextensible flows of curves in 4-dimensional Galilean space, Math.Sci. Appl. E-Notes , 1, (2013), 28-34.
• [16] O. Roschel, Die Geometrie des Galileischen Raumes, Habilitationsschrift, Leoben, 1984.
• [17] D.J. Unger, Developable surfaces in elastoplastic fracture mechanics, Int. J. Fract., 50, (1991), 33-38.
• [18] I.M. Yaglom, A Simple Non-Euclidean Geometry and Its Physical Basis, Springer-Verlag, New York, 1979.
• [19] O.G. Yildiz, S. Ersoy and M. Masal, A note on inextensible flows of curves on oriented surface, CUBO A Math. Journal, 16, (2014), 11-19.