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Surfaces of revolution with pointwise 1-type Gauss map in pseudo-Galilean space

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In this paper, we study surfaces of revolution in the three dimensional pseudo-Galilean space. We classify surfaces of revolution generated by a non-isotropic curve in terms of the Gauss map and the Laplacian of the surface. Furthermore, we give the classification of surfaces of revolution generated by an isotropic curve satisfying pointwise 1-type Gauss map equation.

Abstract

In this paper, we study surfaces of revolution in the three dimensional pseudo-Galilean space. We classify surfaces of revolution generated by a non-isotropic curve in terms of the Gauss map and the Laplacian of the surface. Furthermore, we give the classification of surfaces of revolution generated by an isotropic curve satisfying pointwise 1-type Gauss map equation.

참고문헌 (12)

  1. Kadri Arslan, "MERIDIAN SURFACES IN E4 WITH POINTWISE 1-TYPE GAUSS MAP", 대한수학회보, 51(3), pp.911~922 (2014), 대한수학회
  2. B. -Y. Chen, "Total Mean Curvature and Submanifolds of Finite Type" (1984), World Scientific Publ.
  3. Bang-Yen Chen, "SURFACES OF REVOLUTION WITH POINTWISE 1-TYPE GAUSS MAP", 대한수학회지, 42(3), pp.447~455 (2005), 대한수학회
  4. B.-Y. Chen, "Submanifolds with finite type Gauss map", Bull. Austral. Math. Soc, 35(2), pp.161~186 (1987)
  5. M. Choi, "Circular cone and its Gauss map", Colloq. Math, 129(2), pp.203~210 (2012)
  6. U. Dursun, "Spacelike rotational surfaces of elliptic, hyperbolic and para-bolic types in Minkowski space E41with pointwise 1-type Gauss map", Math. Phys. Anal. Geom, 17(1-2), pp.247~263 (2014)
  7. U. Dursun, "General rotational surfaces in Euclidean space E4 with pointwise 1-type Gauss map", Math. Commun, 17(1), pp.71~81 (2012)
  8. U.-H. Ki, "Surfaces of revolution with pointwise 1-type Gauss map in Minkowski 3-space", Taiwanese J. Math, 13(1), pp.317~338 (2009)
  9. Y. H. Kim, "Ruled surfaces with pointwise 1-type Gauss map", J. Geom. Phys, 34(3-4), pp.191~205 (2000)
  10. O. Roschel, "Die Geometrie des Galileischen Raumes, Habilitationsschrift" (1984), Institut fur Math. und Angew. Geometrie
  11. Z. M. Sipus, "Surfaces of constant curvature in the pseudo-Galilean space", Int. J. Math. Math. Sci, 2012, pp.1~28 (2012)
  12. D. W. Yoon, "Surfaces of revolution in the three dimensional pseudo-Galilean space", Glas. Mat. Ser. III, 48(68)(2), pp.415~428 (2013)

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