ON THE GAUSS MAP OF GENERALIZED SLANT CYLINDRICAL SURFACES
1
조회
0
다운로드
3
인용
0
참고문헌
키워드
초록
In this article, we study the Gauss map of generalized slant cylindrical surfaces (GSCS's) in the 3-dimensional Euclidean space E^3. 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 ∆G = AG for some 3 £ 3 matrix A are the planes, the spheres and the circular cylinders.
Abstract
In this article, we study the Gauss map of generalized slant cylindrical surfaces (GSCS's) in the 3-dimensional Euclidean space E^3. 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 ∆G = AG for some 3 £ 3 matrix A are the planes, the spheres and the circular cylinders.
참고문헌 (14)
- C. Baikoussis, "On the Gauss map of ruled surfaces", Glasgow Math. J, 34, pp.355~359 (1992)
- C. Baikoussis, "Ruled surfaces and tubes with finite type Gauss map", Tokyo J. Math, 16, pp.341~348 (1993)
- B.-Y. Chen, "Total mean curvature and submanifolds of finite type" (1984), World Scientic Publ.
- B.-Y. Chen, "Finite type submanifolds and generalizations", pp.1985
- Bang-Yen Chen, "SURFACES OF REVOLUTION WITH POINTWISE 1-TYPE GAUSS MAP", 대한수학회지, 42(3), pp.447~455 (2005), 대한수학회
- B.-Y. Chen, "Submanifolds with finite type Gauss map", Bull. Austral. Math. Soc, 35, pp.161~186 (1987)
- F. Dillen, "On the Gauss map of surfaces of revolution", Bull. Inst. Math. Acad. Sinica, 18(3), pp.239~246 (1990)
- U. Dursun, "Hypersurfaces with pointwise 1-type Gauss map", Taiwanese J. Math, 11(5), pp.1407~1416 (2007)
- U. Dursun, "Flat surfaces in the Euclidean space E3 with pointwise 1-type Gauss map", Bull. Malays. Math. Sci. Soc.(2), 33(3), pp.469~478 (2010)
- 김동수, "SURFACES WITH POINTWISE 1-TYPE GAUSS MAP", 순수 및 응용수학, 18(4), pp.369~377 (2011), 한국수학교육학회
- 김동수, "SURFACES WITH POINTWISE 1-TYPE GAUSS MAP OF THE SECOND KIND", 순수 및 응용수학, 19(3), pp.229~237 (2012), 한국수학교육학회[DOI]
- 김동수, "SURFACES WITH PLANAR LINES OF CURVATURE", 호남수학학술지, 32(4), pp.777~790 (2010), 호남수학회
- Y.H. Kim, "On the Gauss map of ruled surfaces in Minkowski space", Rocky Mountain J. Math, 35(5), pp.1555~1581 (2005)
- E.A. Ruh, "The tension field of the Gauss map", Trans. Amer. Math. Soc, 149, pp.569~573 (1970)