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Year 2017, Volume: 5 Issue: 4, 72 - 79, 01.10.2017

Abstract

References

  • C. Baikoussis, D.E. Blair; On the Gauss map of ruled surfaces, Glasgow Math. J. 34, 355-359, 1992.
  • S. Cengiz, E. B. Koç Öztürk and U. Öztürk; Motions of Curves in the Pseudo-Galilean Space G_3^1, Mathematical Problems in Engineering, http://dx.doi.org/10.1155/2015/150685, 2015.
  • D. Cervone; A tight polyhedral immersion of the twisted surface of Euler characteristic -3, Topology 40, 571 – 584, 2001.
  • B. Y. Chen, M. Choi, Y.H. Kim; Surfaces of revolution with pointwise 1-type Gauss map, J. Korean Math. Soc. 42(3), 447-455, 2005.
  • B. Y. Chen, S. Ishikawa; On classification of some surfaces of revolution of finite type, Tsukuba J. Math. 17, 287-298, 1993.
  • B. Divjak; Curves in Pseudo-Galilean geometry, Ann. Univ. Sci. Budapest. Eötvös Sect. Math. 41, 117-128, 1998.
  • B. Divjak and Z. M. Sipus; Some special surfaces in the pseudo-Galilean space, Acta Math. Hungar. 118, 209–226, 2008.
  • W. Goemans and I. V. de Woestyne; Twisted surfaces in Euclidean and Minkowski 3-space, Pure and Applied Differential Geometry, 143–151, 2013.
  • W. Goemans and I. V. de Woestyne; Twisted Surfaces with Null Rotation Axis in Minkowski 3-Space, Results. Math., DOI 10.1007/s00025-015-0462-2, 2015.
  • W. Goemans and I. V. de Woestyne; Constant curvature twisted surfaces in 3-dimensional Euclidean and Minkowski space. In: Proceedings of the Conference RIGA 2014. Riemannian Geometry and Applications to Engineering and Economics, pp. 117–130. Bucharest, 2014.
  • A. Kazan, H. B. Karadağ; A Classification of Surfaces of Revolution in Lorentz-Minkowski Space, Int. J. Contemp. Math. Sciences 6(39), 1915-1928, 2011.
  • A. Kazan, H. B. Karadağ; Surfaces of Revolution in Minkowski 3-Space Satisfying Γ ̃_11^1 (G)=k(G+C), J. of Math. and System Sci. 3, 567-572, 2013.
  • Y. H. Kim; Ruled surfaces and their Gauss maps in Lorentz-Minkowski spaces, Information Center for Mathematical Sciences 5(2), 97-104, 2002.
  • Z. M. Sipus and B. Divjak; Surfaces of Constant Curvature in the Pseudo-Galilean Space, Int. J. of Math. and Math. Sci., doi:10.1155/2012/375264, 2012.
  • D. W. Yoon; Surfaces of Revolution in the Three Dimensional Pseudo-Galilean Space, Glasnik Matematicki 48(68), 415 – 428, 2013.
  • D. W. Yoon; On the Gauss map of Tubular Surfaces in Galilean 3-space, Int. J. of Math. Analysis 8(45), 2229-2238, 2014.
  • D. W. Yoon; Some Classification of Translation Surfaces in Galilean 3-Space, Int. J. of Math. Analysis 6(28), 1355-1361, 2012.

Twisted Surfaces in the Pseudo-Galilean Space

Year 2017, Volume: 5 Issue: 4, 72 - 79, 01.10.2017

Abstract

In this paper, we construct the twisted surfaces according to the supporting plane and type of rotations in pseudo-Galilean space G31. Also, we find the Gaussian curvatures and mean curvatures of the different types of these twisted surfaces and draw some figures for these twisted surfaces.

References

  • C. Baikoussis, D.E. Blair; On the Gauss map of ruled surfaces, Glasgow Math. J. 34, 355-359, 1992.
  • S. Cengiz, E. B. Koç Öztürk and U. Öztürk; Motions of Curves in the Pseudo-Galilean Space G_3^1, Mathematical Problems in Engineering, http://dx.doi.org/10.1155/2015/150685, 2015.
  • D. Cervone; A tight polyhedral immersion of the twisted surface of Euler characteristic -3, Topology 40, 571 – 584, 2001.
  • B. Y. Chen, M. Choi, Y.H. Kim; Surfaces of revolution with pointwise 1-type Gauss map, J. Korean Math. Soc. 42(3), 447-455, 2005.
  • B. Y. Chen, S. Ishikawa; On classification of some surfaces of revolution of finite type, Tsukuba J. Math. 17, 287-298, 1993.
  • B. Divjak; Curves in Pseudo-Galilean geometry, Ann. Univ. Sci. Budapest. Eötvös Sect. Math. 41, 117-128, 1998.
  • B. Divjak and Z. M. Sipus; Some special surfaces in the pseudo-Galilean space, Acta Math. Hungar. 118, 209–226, 2008.
  • W. Goemans and I. V. de Woestyne; Twisted surfaces in Euclidean and Minkowski 3-space, Pure and Applied Differential Geometry, 143–151, 2013.
  • W. Goemans and I. V. de Woestyne; Twisted Surfaces with Null Rotation Axis in Minkowski 3-Space, Results. Math., DOI 10.1007/s00025-015-0462-2, 2015.
  • W. Goemans and I. V. de Woestyne; Constant curvature twisted surfaces in 3-dimensional Euclidean and Minkowski space. In: Proceedings of the Conference RIGA 2014. Riemannian Geometry and Applications to Engineering and Economics, pp. 117–130. Bucharest, 2014.
  • A. Kazan, H. B. Karadağ; A Classification of Surfaces of Revolution in Lorentz-Minkowski Space, Int. J. Contemp. Math. Sciences 6(39), 1915-1928, 2011.
  • A. Kazan, H. B. Karadağ; Surfaces of Revolution in Minkowski 3-Space Satisfying Γ ̃_11^1 (G)=k(G+C), J. of Math. and System Sci. 3, 567-572, 2013.
  • Y. H. Kim; Ruled surfaces and their Gauss maps in Lorentz-Minkowski spaces, Information Center for Mathematical Sciences 5(2), 97-104, 2002.
  • Z. M. Sipus and B. Divjak; Surfaces of Constant Curvature in the Pseudo-Galilean Space, Int. J. of Math. and Math. Sci., doi:10.1155/2012/375264, 2012.
  • D. W. Yoon; Surfaces of Revolution in the Three Dimensional Pseudo-Galilean Space, Glasnik Matematicki 48(68), 415 – 428, 2013.
  • D. W. Yoon; On the Gauss map of Tubular Surfaces in Galilean 3-space, Int. J. of Math. Analysis 8(45), 2229-2238, 2014.
  • D. W. Yoon; Some Classification of Translation Surfaces in Galilean 3-Space, Int. J. of Math. Analysis 6(28), 1355-1361, 2012.
There are 17 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Ahmet Kazan This is me

H. Bayram Karadag This is me

Publication Date October 1, 2017
Published in Issue Year 2017 Volume: 5 Issue: 4

Cite

APA Kazan, A., & Karadag, H. B. (2017). Twisted Surfaces in the Pseudo-Galilean Space. New Trends in Mathematical Sciences, 5(4), 72-79.
AMA Kazan A, Karadag HB. Twisted Surfaces in the Pseudo-Galilean Space. New Trends in Mathematical Sciences. October 2017;5(4):72-79.
Chicago Kazan, Ahmet, and H. Bayram Karadag. “Twisted Surfaces in the Pseudo-Galilean Space”. New Trends in Mathematical Sciences 5, no. 4 (October 2017): 72-79.
EndNote Kazan A, Karadag HB (October 1, 2017) Twisted Surfaces in the Pseudo-Galilean Space. New Trends in Mathematical Sciences 5 4 72–79.
IEEE A. Kazan and H. B. Karadag, “Twisted Surfaces in the Pseudo-Galilean Space”, New Trends in Mathematical Sciences, vol. 5, no. 4, pp. 72–79, 2017.
ISNAD Kazan, Ahmet - Karadag, H. Bayram. “Twisted Surfaces in the Pseudo-Galilean Space”. New Trends in Mathematical Sciences 5/4 (October 2017), 72-79.
JAMA Kazan A, Karadag HB. Twisted Surfaces in the Pseudo-Galilean Space. New Trends in Mathematical Sciences. 2017;5:72–79.
MLA Kazan, Ahmet and H. Bayram Karadag. “Twisted Surfaces in the Pseudo-Galilean Space”. New Trends in Mathematical Sciences, vol. 5, no. 4, 2017, pp. 72-79.
Vancouver Kazan A, Karadag HB. Twisted Surfaces in the Pseudo-Galilean Space. New Trends in Mathematical Sciences. 2017;5(4):72-9.