바로가기메뉴

본문 바로가기 주메뉴 바로가기

logo

  • P-ISSN1226-0657
  • E-ISSN2287-6081
  • KCI

ISSN : 1226-0657

Article Contents

Prev Next
e-Submission

Vol.20 No.3

Citation Share

ON THE GAUSS MAP OF GENERALIZED SLANT CYLINDRICAL SURFACES

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081
2013, v.20 no.3, pp.149-158
https://doi.org/10.7468/jksmeb.2013.20.3.149
Kim, Dong-Soo
Song, Booseon
Kim,, D. , & Song,, B. (2013). ON THE GAUSS MAP OF GENERALIZED SLANT CYLINDRICAL SURFACES. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 20(3), 149-158, https://doi.org/10.7468/jksmeb.2013.20.3.149

Abstract

In this article, we study the Gauss map of generalized slant cylindrical surfaces (GSCS's) in the 3-dimensional Euclidean space <TEX>$\mathbb{E}^3$</TEX>. Surfaces of revolution, cylindrical surfaces and tubes along a plane curve are special cases of GSCS's. Our main results state that the only GSCS's with Gauss map G satisfying <TEX>${\Delta}G=AG$</TEX> for some <TEX>$3{\times}3$</TEX> matrix A are the planes, the spheres and the circular cylinders.

keywords
Gauss map, Laplace operator, surface of rotation, cylindrical surface, slant cylindrical surface, generalized slant cylindrical surface

Reference

1.

(1990). On the Gauss map of surfaces of revolution. Bull. Inst. Math. Acad. Sinica, 18(3), 239-246.

2.

(1992). On the Gauss map of ruled surfaces. Glasgow Math. J., 34, 355-359. 10.1017/S0017089500008946.

3.

(1993). Ruled surfaces and tubes with finite type Gauss map. Tokyo J. Math., 16, 341-348. 10.3836/tjm/1270128488.

4.

Total mean curvature and submanifolds of finite type.

5.

Finite type submanifolds and generalizations.

6.

(2005). SURFACES OF REVOLUTION WITH POINTWISE 1-TYPE GAUSS MAP. Journal of the Korean Mathematical Society, 42(3), 447-455. 10.4134/JKMS.2005.42.3.447.

7.

(1987). Submanifolds with finite type Gauss map. Bull. Austral. Math. Soc., 35, 161-186. 10.1017/S0004972700013162.

8.

(2007). Hypersurfaces with pointwise 1-type Gauss map. Taiwanese J. Math., 11(5), 1407-1416.

9.

(2010). Flat surfaces in the Euclidean space E3 with pointwise 1-type Gauss map. Bull. Malays. Math. Sci. Soc.(2), 33(3), 469-478.

10.

(2011). SURFACES WITH POINTWISE 1-TYPE GAUSS MAP. The Pure and Applied Mathematics, 18(4), 369-377. 10.7468/jksmeb.2011.18.4.369.

11.

(2012). SURFACES WITH POINTWISE 1-TYPE GAUSS MAP OF THE SECOND KIND. The Pure and Applied Mathematics, 19(3), 229-237. 10.7468/jksmeb.2012.19.3.229.

12.

(2010). SURFACES WITH PLANAR LINES OF CURVATURE. Honam Mathematical Journal, 32(4), 777-790. 10.5831/HMJ.2010.32.4.777.

13.

(2005). On the Gauss map of ruled surfaces in Minkowski space. Rocky Mountain J. Math., 35(5), 1555-1581. 10.1216/rmjm/1181069651.

14.

(1970). The tension field of the Gauss map. Trans. Amer. Math. Soc., 149, 569-573. 10.1090/S0002-9947-1970-0259768-5.

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics

e-Submission OA Policy