Twisted Surfaces in the Pseudo-Galilean Space

Twisted Surfaces in the Pseudo-Galilean Space

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.

___

  • 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.