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Year 2019, Volume: 2 Issue: 2, 148 - 152, 25.11.2019

Mustafa Dede , Cumali Ekici

Abstract

References

  • [1] M. Dede, Tubular surfaces in Galilean space, Math. Commun., 18 (2013), 209-217.
  • [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] B. Divjak, Curves in pseudo-Galilean geometry, Annales Universitatis Scientiarum Budapest, 41 (1998), 117-128.
  • [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] B. Divjak, Z. Milin-Sipus, Minding isometries of ruled surfaces in pseudo-Galilean space, J. Geom.,77 (2003), 35-47.
  • [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] H. W. Guggenheimer, Differential geometry, New York: McGraw-Hill, 1963.
  • [8] I. Kamenarovic, Existence theorems for ruled surfaces in the Galilean Space G3, Rad HAZU Math., 456 (1991), 183-196.
  • [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] Z. Milin-Sipus, Ruled Weingarten surfaces in Galilean space, Periodica Mathematica Hungarica, 56 (2008), 213-225.
  • [11] B. Ravani, T.S. Ku, Bertrand Offsets of ruled and developable surfaces, Comp. Aided Geom. Design,23 (1991), 145-152.
  • [12] O. M. Röschel, Die geometrie des Galileischen raumes, Leoben: Habilitationsschrift, 1984.
  • [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] A. Turgut, H. H. Hacısaliho˘glu, Timelike ruled surfaces in the Minkowski 3-space, Far East J. Math. Sci.,5 (1997), 83-90.
  • [15] A. Turgut, H. H. Hacısaliho˘glu, Timelike ruled surfaces in the Minkowski 3-space II, Turkish J. Math. 22 (1998), 33-46.
  • [16] I. M. A. Yaglom, Simple non-Euclidean geometry and its physical basis, New York: Springer-Verlag, 1979.
  • [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.

On Developable Ruled Surfaces in Pseudo-Galilean Space

Year 2019, Volume: 2 Issue: 2, 148 - 152, 25.11.2019

Mustafa Dede , Cumali Ekici

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] M. Dede, Tubular surfaces in Galilean space, Math. Commun., 18 (2013), 209-217.
  • [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] B. Divjak, Curves in pseudo-Galilean geometry, Annales Universitatis Scientiarum Budapest, 41 (1998), 117-128.
  • [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] B. Divjak, Z. Milin-Sipus, Minding isometries of ruled surfaces in pseudo-Galilean space, J. Geom.,77 (2003), 35-47.
  • [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] H. W. Guggenheimer, Differential geometry, New York: McGraw-Hill, 1963.
  • [8] I. Kamenarovic, Existence theorems for ruled surfaces in the Galilean Space G3, Rad HAZU Math., 456 (1991), 183-196.
  • [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] Z. Milin-Sipus, Ruled Weingarten surfaces in Galilean space, Periodica Mathematica Hungarica, 56 (2008), 213-225.
  • [11] B. Ravani, T.S. Ku, Bertrand Offsets of ruled and developable surfaces, Comp. Aided Geom. Design,23 (1991), 145-152.
  • [12] O. M. Röschel, Die geometrie des Galileischen raumes, Leoben: Habilitationsschrift, 1984.
  • [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] A. Turgut, H. H. Hacısaliho˘glu, Timelike ruled surfaces in the Minkowski 3-space, Far East J. Math. Sci.,5 (1997), 83-90.
  • [15] A. Turgut, H. H. Hacısaliho˘glu, Timelike ruled surfaces in the Minkowski 3-space II, Turkish J. Math. 22 (1998), 33-46.
  • [16] I. M. A. Yaglom, Simple non-Euclidean geometry and its physical basis, New York: Springer-Verlag, 1979.
  • [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.
There are 17 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Mustafa Dede 0000-0003-2652-637X

Cumali Ekici

Publication Date November 25, 2019
Acceptance Date September 27, 2019
Published in Issue Year 2019 Volume: 2 Issue: 2

Cite

APA Dede, M., & Ekici, C. (2019). On Developable Ruled Surfaces in Pseudo-Galilean Space. Conference Proceedings of Science and Technology, 2(2), 148-152.
AMA Dede M, Ekici C. On Developable Ruled Surfaces in Pseudo-Galilean Space. Conference Proceedings of Science and Technology. November 2019;2(2):148-152.
Chicago Dede, Mustafa, and Cumali Ekici. “On Developable Ruled Surfaces in Pseudo-Galilean Space”. Conference Proceedings of Science and Technology 2, no. 2 (November 2019): 148-52.
EndNote Dede M, Ekici C (November 1, 2019) On Developable Ruled Surfaces in Pseudo-Galilean Space. Conference Proceedings of Science and Technology 2 2 148–152.
IEEE M. Dede and C. Ekici, “On Developable Ruled Surfaces in Pseudo-Galilean Space”, Conference Proceedings of Science and Technology, vol. 2, no. 2, pp. 148–152, 2019.
ISNAD Dede, Mustafa - Ekici, Cumali. “On Developable Ruled Surfaces in Pseudo-Galilean Space”. Conference Proceedings of Science and Technology 2/2 (November 2019), 148-152.
JAMA Dede M, Ekici C. On Developable Ruled Surfaces in Pseudo-Galilean Space. Conference Proceedings of Science and Technology. 2019;2:148–152.
MLA Dede, Mustafa and Cumali Ekici. “On Developable Ruled Surfaces in Pseudo-Galilean Space”. Conference Proceedings of Science and Technology, vol. 2, no. 2, 2019, pp. 148-52.
Vancouver Dede M, Ekici C. On Developable Ruled Surfaces in Pseudo-Galilean Space. Conference Proceedings of Science and Technology. 2019;2(2):148-52.
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