Gauss maps of ruled submanifolds and applications I
1
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
As a generalizing certain geometric property occurred on the helicoid of 3-dimensional Euclidean space regarding the Gauss map, we study ruled submanifolds in a Euclidean space with pointwise 1-type Gauss map of the first kind. In this paper, as new examples of cylindrical ruled submanifolds in Euclidean space, we construct generalized circular cylinders and characterize such ruled submanifolds and minimal ruled submanifolds of Euclidean space with pointwise 1-type Gauss map of the first kind.
Abstract
As a generalizing certain geometric property occurred on the helicoid of 3-dimensional Euclidean space regarding the Gauss map, we study ruled submanifolds in a Euclidean space with pointwise 1-type Gauss map of the first kind. In this paper, as new examples of cylindrical ruled submanifolds in Euclidean space, we construct generalized circular cylinders and characterize such ruled submanifolds and minimal ruled submanifolds of Euclidean space with pointwise 1-type Gauss map of the first kind.
참고문헌 (22)
- J. M. Barbosa, "Minimal ruled submanifolds in spaces of constant curvature", Indiana Univ. Math. J, 33(4), pp.531~547 (1984)
- B.-Y. Chen, "Total Mean Curvature and Submanifolds of Finite Type" (2015), World Scientific
- Bang-Yen Chen, "SURFACES OF REVOLUTION WITH POINTWISE 1-TYPE GAUSS MAP", 대한수학회지, 42(3), pp.447~455 (2005), 대한수학회
- B.-Y. Chen, "Ruled surfaces of finite type", Bull. Austral. Math. Soc, 42(3), pp.447~453 (1990)
- B.-Y. Chen, "Submanifolds with finite type Gauss map", Bull. Austral. Math. Soc, 35(2), pp.161~186 (1987)
- M. Choi, "Circular cone and its Gauss map", Colloq. Math, 129(2), pp.203~210 (2012)
- M. Choi, "Characterization of the helicoid as ruled surfaces with pointwise 1-type Gauss map", Bull. Korean Math. Soc, 38(4), pp.753~761 (2001)
- M. Choi, "Classification of ruled surfaces with pointwise 1-type Gauss map", Taiwanese J. Math, 14(4), pp.1297~1308 (2010)
- F. Dillen, "Ruled submanifolds of finite type", Proc. Amer. Math. Soc, 114(3), pp.795~798 (1992)
- 김동수, "Ruled Surfaces of Finite Type in Lorentzian Space-times", 호남수학학술지, 31(2), pp.177~183 (2009), 호남수학회
- 김동수, "RULED SUBMANIFOLDS OF FINITE TYPE IN LORENTZIAN SPACE-TIMES", 호남수학학술지, 32(2), pp.261~269 (2010), 호남수학회
- 김동수, "FINITE TYPE RULED HYPERSURFACES IN LORENTZ-MINKOWSKI SPACE", 호남수학학술지, 30(4), pp.743~748 (2008), 호남수학회
- D.-S. Kim, "Some classification results on finite type ruled submanifolds in a LorentzMinkowski space", Taiwanese J. Math, 16(4), pp.1475~1488 (2012)
- D.-S. Kim, "Minimal ruled submanifolds in Minkowski space Lm", J. Geom. Phys, 62(9), pp.1893~1902 (2012)
- D.-S. Kim, "Ruled submanifolds with Harmonic Gauss map", Taiwanese J. Math, 18(1), pp.53~76 (2014)
- D.-S. Kim, "Some classifications of ruled submanifolds in Minkowski space and their Gauss map", Taiwanese J. Math, 18(4), pp.10221~11040 (2014)
- D.-S. Kim, "Extended B-scrolls and their Gauss maps", Indian J. Pure Appl. Math, 33(7), pp.1031~1040 (2002)
- D.-S. Kim, "Characterization of generalized B-scrolls and cylinders over finite type curves", Indian J. Pure Appl. Math, 33(11), pp.1523~1532 (2003)
- D.-S. Kim, "Finite type ruled surfaces in Lorentz-Minkowski space", Taiwanese J. Math, 11(1), pp.1~13 (2007)
- Y. H. Kim, "Ruled surfaces with finite type Gauss map in Minkowski spaces", Soochow J. Math, 26(1), pp.85~96 (2000)
- Y. H. Kim, "Ruled surfaces with pointwise 1-type Gauss maps", J. Geom. Phys, 34(3-4), pp.191~205 (2000)
- Y. H. Kim, "On the Gauss map of ruled surfaces in Minkowski space", Rocky Mountain J. Math, 35(5), pp.1555~1581 (2005)