ON THE GAUSS MAP OF SURFACES OF REVOLUTION WITHOUT PARABOLIC POINTS

Kim, Young-Ho; Lee, Chul-Woo; Yoon, Dae-Won

doi:10.4134/BKMS.2009.46.6.1141

HOME > Journal Browse > About Journal > Journal Vol & Issue > Full Record

ON THE GAUSS MAP OF SURFACES OF REVOLUTION WITHOUT PARABOLIC POINTS

Journal title : Bulletin of the Korean Mathematical Society
Volume 46, Issue 6, 2009, pp.1141-1149
Publisher : The Korean Mathematical Society
DOI : 10.4134/BKMS.2009.46.6.1141

Title & Authors

ON THE GAUSS MAP OF SURFACES OF REVOLUTION WITHOUT PARABOLIC POINTS
Kim, Young-Ho; Lee, Chul-Woo; Yoon, Dae-Won;

Abstract

In this article, we study surfaces of revolution without parabolic points in a Euclidean 3-space whose Gauss map G satisfies the condition ${\Delta}^hG\;

Keywords

Gauss map;surface of revolution;Laplace operator;second fundamental form;

Language

English

Cited by

1time(s) in KSCD

SURFACES OF REVOLUTION SATISFYING Δ^IIG = f(G + C),;;

대한수학회보, 2013. vol.50. 4, pp.1061-1067

4time(s) in CrossRef

SURFACES OF REVOLUTION SATISFYING ΔIIG = f(G + C), Bulletin of the Korean Mathematical Society, 2013, 50, 4, 1061

On the Gauss Map of Surfaces of Revolution with Lightlike Axis in Minkowski 3-Space, Journal of Function Spaces and Applications, 2013, 2013, 1

Classification of rotational surfaces in pseudo-Galilean space, Glasnik Matematicki, 2015, 50, 2, 453

SURFACES OF REVOLUTION WITH LIGHT-LIKE AXIS, Journal of the Chungcheong Mathematical Society , 2012, 25, 4, 677

References

R. Aiyama, On the Gauss map of complete space-like hypersurfaces of constant mean curvature in Minkowski space, Tsukuba J. Math. 16 (1992), no. 2, 353-361

L. J. Alias, A. Ferr´andez, P. Lucas, and M. A. Mero.no, On the Gauss map of B-scrolls, Tsukuba J. Math. 22 (1998), no. 2, 371-377

C. Baikoussis and D. E. Blair, On the Gauss map of ruled surfaces, Glasgow Math. J. 34 (1992), no. 3, 355-359

C. Baikoussis and L. Verstraelen, On the Gauss map of helicoidal surfaces, Rend. Sem. Mat. Messina Ser. II 2(16) (1993), 31-42

C. Baikoussis and L. Verstraelen, The Chen-type of the spiral surfaces, Results Math. 28 (1995), no. 3-4, 214-223

B. Y. Chen, A report on submanifolds of finite type, Soochow J. Math. 22 (1996), no. 2, 117-337

S. M. Choi, On the Gauss map of surfaces of revolution in a 3-dimensional Minkowski space, Tsukuba J. Math. 19 (1995), no. 2, 351-367

S. M. Choi, On the Gauss map of ruled surfaces in a 3-dimensional Minkowski space, Tsukuba J. Math. 19 (1995), no. 2, 285–304

F. Dillen, J. Pas, and L. Verstralen, On the Gauss map of surfaces of revolution, Bull. Inst. Math. Acad. Sinica 18 (1990), no. 3, 239-246

10.

D.-S. Kim, Y. H. Kim, and D. W. Yoon, Extended B-scrolls and their Gauss maps, Indian J. Pure Appl. Math. 33 (2002), no. 7, 1031-1040

11.

Y. H. Kim and D. W. Yoon, Classifications of rotation surfaces in pseudo-Euclidean space, J. Korean Math. Soc. 41 (2004), no. 2, 379-396

12.

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

13.

Y. H. Kim and D. W. Yoon, On the Gauss map of ruled surfaces in Minkowski space, Rocky Mountain J. Math. 35 (2005), no. 5, 1555-1581

14.

E. A. Ruh and J. Vilms, The tension field of the Gauss map, Trans. Amer. Math. Soc. 149 (1970), 569-573

15.

D. W. Yoon, On the Gauss map of translation surfaces in Minkowski 3-space, Taiwanese J. Math. 6 (2002), no. 3, 389-398

16.

D. W. Yoon, Rotation surfaces with finite type Gauss map in $E^4$, Indian J. Pure Appl. Math. 32 (2001), no. 12, 1803-1808