Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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SURFACES OF REVOLUTION WITH POINTWISE 1-TYPE GAUSS MAP IN PSEUDO-GALILEAN SPACE

  • Choi, Miekyung (Department of Mathematics Education, Gyeongsang National University) ;
  • Yoon, Dae Won (Department of Mathematics Education and RINS, Gyeongsang National University)
  • Received : 2015.03.02
  • Published : 2016.03.31
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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.

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Acknowledgement

Supported by : Gyeongsang National University

References

  1. K. Arslan, B. Bulca, and V. Milousheva, Meridian surfaces in $\mathbb{E}^4$ with pointwise 1-type Gauss map, Bull. Korean Math. Soc. 51 (2014), no. 3, 911-922. https://doi.org/10.4134/BKMS.2014.51.3.911
  2. B.-Y. Chen, Total Mean Curvature and Submanifolds of Finite Type, World Scientific Publ., 1984.
  3. B.-Y. Chen, M. Choi, and Y. H. Kim, Surfaces of revolution with pointwise 1-type Gauss map, J. Korean Math. Soc. 42 (2005), no. 3, 447-455. https://doi.org/10.4134/JKMS.2005.42.3.447
  4. B.-Y. Chen and P. Piccinni, Submanifolds with finite type Gauss map, Bull. Austral. Math. Soc. 35 (1987), no. 2, 161-186. https://doi.org/10.1017/S0004972700013162
  5. M. Choi, D.-S. Kim, Y. H. Kim, and D. W. Yoon, Circular cone and its Gauss map, Colloq. Math. 129 (2012), no. 2, 203-210. https://doi.org/10.4064/cm129-2-4
  6. U. Dursun and B. Bektas, Spacelike rotational surfaces of elliptic, hyperbolic and para-bolic types in Minkowski space ${\mathbb{E}}^4_1$ with pointwise 1-type Gauss map, Math. Phys. Anal. Geom. 17 (2014), no. 1-2, 247-263. https://doi.org/10.1007/s11040-014-9153-6
  7. U. Dursun and N. C. Turgay, General rotational surfaces in Euclidean space $\mathbb{E}4$ with pointwise 1-type Gauss map, Math. Commun. 17 (2012), no. 1, 71-81.
  8. U.-H. Ki, D.-S. Kim, Y. H. Kim, and Y.-M. Roh, Surfaces of revolution with pointwise 1-type Gauss map in Minkowski 3-space, Taiwanese J. Math. 13 (2009), no. 1, 317-338. https://doi.org/10.11650/twjm/1500405286
  9. Y. H. Kim and D. W. Yoon, Ruled surfaces with pointwise 1-type Gauss map, J. Geom. Phys. 34 (2000), no. 3-4, 191-205. https://doi.org/10.1016/S0393-0440(99)00063-7
  10. O. Roschel, Die Geometrie des Galileischen Raumes, Habilitationsschrift, Institut fur Math. und Angew. Geometrie, Leoben, 1984.
  11. Z. M. Sipus and B. Divjak, Surfaces of constant curvature in the pseudo-Galilean space, Int. J. Math. Math. Sci. 2012 (2012), 1-28.
  12. D. W. Yoon, Surfaces of revolution in the three dimensional pseudo-Galilean space, Glas. Mat. Ser. III 48(68) (2013), no. 2, 415-428. https://doi.org/10.3336/gm.48.2.13