INEXTENSIBLE FLOWS OF CURVES IN THE EQUIFORM GEOMETRY OF THE PSEUDO-GALILEAN SPACE G13

Year 2016, Volume: 6 Issue: 2, 175 - 184, 01.12.2016

Handan Öztekin Hülya Gün Bozok

Abstract

In this paper, we study inextensible ows of curves in 3-dimensional pseudo- Galilean space. We give necessary and sucient conditions for inextensible ows of curves according to equiform geometry in pseudo-Galilean space.

Keywords

inextensible ows, equiform dierential geometry, Galilean space, pseudo- Galilean space.

References

• Desbrun,M. and Cani-Gascuel,M.P., (1998), Active implicit surface for animation, Proc. Graphics Interface-Canadian Inf. Process. Soc., pp.143-150.
• Divjak,B., (2003), Special curves on ruled surfaces in Galilean and pseudo-Galilean space, Acta Math. Hungar. 98(3), pp. 203-215.
• Divjak,B., (1998), Curves in pseudo-Galilean geometry, Annales Univ. Sci. Budapest, 41, pp. 117-128.
• Divjak,B. and Milin-Sipus,Z., (2003), Special curves on the ruled surfaces in Galilean and pseudo Galilean space, Acta Math. Hungar., 98(3), pp. 203-215.
• Divjak,B. and Erjavec,Z., (2008), The equiform differential geometry of curves in the pseudo-Galilean space, Mathematical Communitations, 13, pp. 321-331.
• Gage,M. and Hamilton,R.S., (1986), The heat equation shrinking convex plane curves, J. Differential Geom., 23, pp. 69-96.
• Grayson,M., (1987), The heat equation shrinks embedded plane curves to round points, J. Differential Geom., 26, pp. 285-314.
• Kass,M., Witkin,A. and Terzopoulos,D., (1987), Snakes: active contour models, Proc. 1st Int. Con- ference on Computer Vision, pp. 259-268.
• Kwon,D.Y., Park,F.C. and Chi,D.P., (2005), Inextensible flows of curves and developable surfaces,Applied Mathematics Letters, 18, pp. 1156-1162.
• Kwon,D.Y. and Park,F.C., (1999), Evolution of inelastic plane curves, Appl. Math. Lett., 12 pp. 119.
• Latifi,D. and Razavi,A., (2008), Inextensible flows of curves in Minkowskian Space, Adv. Studies Theor. Phys. 2(16), pp. 761-768.
• Lu,H.Q., Todhunter,J.S. and Sze,T.W., (1993), Congruence conditions for nonplanar developable surfaces and their application to surface recognition, CVGIP, Image Underst., 56, pp. 265-285 .
• Ogrenmis,A.O. and Yeneroglu,M., (2010), Inextensible curves in the Galilean space, International Journal of the Physical Sciences, 5(9),pp. 1424-1427.
• Ogrenmis,A.O., Ergut,M. and Bektas,M., (2007), On the Helices in the Galilean Space G3, Iran. J.Sci, Tech. Trans. A Sci., 31(2), pp. 177-181.
• Pavkovic,B.J., (1986), Equiform geometry of curves in the isotropic space I13and I23, Rad JAZU., pp. 44.
• Pavkovic,B.J. and Kamenarovic,I., (1987) ,The equiform differential geometry of curves in the Galilean space G3, Glasnik Mat. 22(42), pp. 449-457.
• Unger,D.J., (1991), Developable surfaces in elastoplastic fracture mechanics, Int. J. Fract., 50, pp. 38.
• Yoon,D.W., (2011), Inelastic flows of curves according to equiform in Galilean space, Journal of the Chungcheong Mathematical Society, 24(4).