Browse > Article
http://dx.doi.org/10.4134/BKMS.2016.53.2.519

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)
Publication Information
Bulletin of the Korean Mathematical Society / v.53, no.2, 2016 , pp. 519-530 More about this Journal
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;
Citations & Related Records
Times Cited By KSCI : 2  (Citation Analysis)
연도 인용수 순위
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.   DOI
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.   DOI
4 B.-Y. Chen and P. Piccinni, Submanifolds with finite type Gauss map, Bull. Austral. Math. Soc. 35 (1987), no. 2, 161-186.   DOI
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.   DOI
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.   DOI
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.   DOI
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.   DOI
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.   DOI