Browse > Article
http://dx.doi.org/10.5831/HMJ.2020.42.4.769

A NOTE ON INEXTENSIBLE FLOWS OF CURVES WITH FERMI-WALKER DERIVATIVE IN GALILEAN SPACE G3  

Bozok, Hulya Gun (Department of Mathematics, Osmaniye Korkut Ata University)
Sertkol, Ipek Nizamettin (Department of Mathematics, Osmaniye Korkut Ata University)
Publication Information
Honam Mathematical Journal / v.42, no.4, 2020 , pp. 769-780 More about this Journal
Abstract
In this paper, Fermi-Walker derivative for inextensible flows of curves are researched in 3-dimensional Galilean space G3. Firstly using Frenet and Darboux frame with the help of Fermi-Walker derivative a new approach for these flows are expressed, then some results are obtained for these flows to be Fermi-Walker transported in G3.
Keywords
Inextensible flows; Fermi-Walker derivative; Galilean space;
Citations & Related Records
연도 인용수 순위
  • Reference
1 G. Altay Suroglu, A Modified Fermi-Walker Derivative for Inextensible Flows of Binormal Spherical Image, Open Phys., 16, (2018), 14-20.   DOI
2 M.S. Berman, Introduction to general relativistic and scalar-tensor cosmologies, Nova Sciences Publishers. Inc., New York, (2007).
3 M. Desbrun, and M.P. Cani-Gascuel, Active implicit surface for animation, in: Proc. Graphics Interface-Canadian Inf. Process. Soc., (1998), 143-150.
4 E. Fermi, Sopra i fenomeni che avvengono in vicinanza di una linea oraria, Atti Accad. Naz. Lincei Cl. Sci. Fiz. Mat. Nat., 31, (1922), 184-306.
5 M. Gage, and R.S. Hamilton, The heat equation shrinking convex plane curves, J. Differential Geom., 23, (1986), 69-96.   DOI
6 M. Grayson, The heat equation shrinks embedded plane curves to round points, J. Differential Geom., 26, (1987), 285-314.   DOI
7 H. Gun Bozok and M. Ergut, Inextensible Flows of Curves According to Darboux Frame in Galilean Space G3, in: Proc. 4th Int. Conference on Computational Mathematics and Engineering Sciences, (2019), 186-192.
8 M. Kass, A. Witkin and D. Terzopoulos, Snakes: active contour models, in: Proc. 1st Int. Conference on Computer Vision, (1987), 259-268.
9 I. Kamenarovic, Existence Theorems for Ruled Surfaces in the Galilean Space G3, Rad HAZU Math. 10, (1991), 183-196.
10 F. Karakus and Y. Yayli, The Fermi-Walker Derivative in Minkowski space E31, Advances in Applied Clifford Algebras, 27, (2017), 1353-1368.   DOI
11 T. Korpinar, On the Fermi-Walker Derivative for Inextensible Flows, Z. Naturforsch, 70(7), (2015), 477-482.   DOI
12 D.Y. Kwon, F.C. Park and D.P. Chi, Inextensible flows of curves and developable surfaces, Applied Mathematics Letters, 18, (2005), 1156-1162.   DOI
13 T. Sahin, Intrinsic equations for a generalized relaxed elastic line on an oriented surface in the Galilean space, Acta Mathematica Scientia, 33B(3), (2013), 701-711.   DOI
14 D. Latifi and A. Razavi, Inextensible flows of curves in Minkowskian Space, Adv. Studies Theor. Phys., 2(16), (2008), 761-768.
15 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.
16 A.O. Ogrenmis and M. Yeneroglu, Inextensible curves in the Galilean space, International Journal of the Physical Sciences, 5(9), (2010), 1424-1427.
17 H. Oztekin and H. Gun Bozok, Inextensible flows of curves in 4-dimensional Galilean space, Math.Sci. Appl. E-Notes, 1(2), (2013), 28-34.
18 O. Roschel, Die Geometrie des Galileischen Raumes, Habilitationsschrift, Leoben,(1984).
19 T. Sahin, F. Karakus and K. Orbay, Parallel Transports with respect to Frenet and Darboux Frames in the Galilean Space, Journal of Science and Arts, 1(50), (2020), 13-24.
20 D.J. Unger, Developable surfaces in elastoplastic fracture mechanics, Int. J. Fract., 50, (1991), 33-38.   DOI