SURFACES OF REVOLUTION WITH POINTWISE 1-TYPE GAUSS MAP IN PSEUDO-GALILEAN SPACE

Title & Authors
SURFACES OF REVOLUTION WITH POINTWISE 1-TYPE GAUSS MAP IN PSEUDO-GALILEAN SPACE
Choi, Miekyung; Yoon, Dae Won;

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.
Keywords
surfaces of revolution;pointwise 1-type Gauss map;pseudo-Galilean space;
Language
English
Cited by
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.

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.

4.
B.-Y. Chen and P. Piccinni, Submanifolds with finite type Gauss map, Bull. Austral. Math. Soc. 35 (1987), no. 2, 161-186.

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.

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.

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.

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.

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.