On Developable Ruled Surfaces in Pseudo-Galilean Space

Abstract

In this paper, we investigated the ruled surfaces in the three-dimensional pseudo-Galilean space. We obtained the distribution parameter of the ruled surface by using the Frenet frame of directrix curve. Moreover, we derived the necessary conditions to construct a developable ruled surface in the pseudo-Galilean space.

Keywords

• Developable,Distribution parameter,Pseudo-Galilean space,Ruled surface

References

1. [1] M. Dede, Tubular surfaces in Galilean space, Math. Commun., 18 (2013), 209-217.
2. [2] M. Dede, C. Ekici, A. C. Cöken, On the parallel surfaces in Galilean space, Hacettepe Journal of Mathematics and Statistics, 42 (2013), 605-615.
3. [3] B. Divjak, Curves in pseudo-Galilean geometry, Annales Universitatis Scientiarum Budapest, 41 (1998), 117-128.
4. [4] B. Divjak, Z. Milin-Sipus, Special curves on ruled surfaces in Galilean and pseudo-Galilean space, Acta Math. Hungar.,98 (2003), 203-215.
5. [5] B. Divjak, Z. Milin-Sipus, Minding isometries of ruled surfaces in pseudo-Galilean space, J. Geom.,77 (2003), 35-47.
6. [6] C. Ekici, M. Dede, On the Darboux vector of ruled surfaces in pseudo-Galilean space, Math. and Comp. App., 16 (2011), 830-838.
7. [7] H. W. Guggenheimer, Differential geometry, New York: McGraw-Hill, 1963.
8. [8] I. Kamenarovic, Existence theorems for ruled surfaces in the Galilean Space G3, Rad HAZU Math., 456 (1991), 183-196.

9. [9] E. Kasap, S. Yüce, N. Kuruo˘glu, The Involute-Evolute Offsets of Ruled Surfaces, Iranian Journal of Science & Technology, Transaction A, 33 (2009), 195-201.
10. [10] Z. Milin-Sipus, Ruled Weingarten surfaces in Galilean space, Periodica Mathematica Hungarica, 56 (2008), 213-225.
11. [11] B. Ravani, T.S. Ku, Bertrand Offsets of ruled and developable surfaces, Comp. Aided Geom. Design,23 (1991), 145-152.
12. [12] O. M. Röschel, Die geometrie des Galileischen raumes, Leoben: Habilitationsschrift, 1984.
13. [13] B. S. Ryuh, G.R. Pennock, Accurate motion of Robot End-Effector using the curvature theory of ruled surfaces, Journal of Mechanisms, Transmissions, and Automation in Design, 10 (1988), 383-387.
14. [14] A. Turgut, H. H. Hacısaliho˘glu, Timelike ruled surfaces in the Minkowski 3-space, Far East J. Math. Sci.,5 (1997), 83-90.
15. [15] A. Turgut, H. H. Hacısaliho˘glu, Timelike ruled surfaces in the Minkowski 3-space II, Turkish J. Math. 22 (1998), 33-46.
16. [16] I. M. A. Yaglom, Simple non-Euclidean geometry and its physical basis, New York: Springer-Verlag, 1979.
17. [17] Y. Yaylı, On the motion of the Frenet vectors and spacelike ruled surfaces in the Minkowski 3-Space, Mathematical & Computational Applications, 5 (2000), 49-55.