ON THE GAUSS MAP OF GENERALIZED SLANT CYLINDRICAL SURFACES

한국수학교육학회지시리즈B:순수및응용수학 / 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 (Department of Mathematics, Chonnam National University)
Song, Booseon (Department of Mathematics, Chonnam National University)

Kim, Dong-Soo, & Song, Booseon. (2013). ON THE GAUSS MAP OF GENERALIZED SLANT CYLINDRICAL SURFACES. 한국수학교육학회지시리즈B:순수및응용수학, 20(3), 149-158, https://doi.org/10.7468/jksmeb.2013.20.3.149

복사

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

참고문헌

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

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

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

Total mean curvature and submanifolds of finite type.

Finite type submanifolds and generalizations.

(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.

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

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

(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.

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논문 상세

Vol.20 No.3

ON THE GAUSS MAP OF GENERALIZED SLANT CYLINDRICAL SURFACES

ON THE GAUSS MAP OF GENERALIZED SLANT CYLINDRICAL SURFACES

Abstract

참고문헌

한국수학교육학회지시리즈B:순수및응용수학