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SURFACES WITH POINTWISE 1-TYPE GAUSS MAP

  • Kim, Dong-Soo (Department of Mathematics, Chonnam National University)
  • 투고 : 2011.09.26
  • 심사 : 2011.10.20
  • 발행 : 2011.11.30

초록

In this article, we study generalized slant cylindrical surfaces (GSCS's) with pointwise 1-type Gauss map of the first and second kinds. Our main results state that GSCS's with pointwise 1-type Gauss map of the first kind coincide with surfaces of revolution with constant mean curvature; and the right cones are the only polynomial kind GSCS's with pointwise 1-type Gauss map of the second kind.

키워드

참고문헌

  1. C. Baikoussis & D. E. Blair: On the Gauss map of ruled surfaces. Glasgow Math. J. 34 (1992), 355-359. https://doi.org/10.1017/S0017089500008946
  2. C. Baikoussis, B.-Y. Chen & L. Verstraelen: Ruled surfaces and tubes with finite type Gauss map. Tokyo J. Math. 16 (1993), 341-348. https://doi.org/10.3836/tjm/1270128488
  3. B.-Y. Chen: Total mean curvature and submanifolds of finite type. World Scientific Publ., New Jersey (1984).
  4. B.-Y. Chen: Finite type submanifolds and generalizations. University of Rome (1985).
  5. B.-Y. Chen, M. Choi & Y.H. Kim: Surfaces of revolution with pointwise 1-type Gauss map. J. Korean Math. Soc. 42 (2005), 447-455. https://doi.org/10.4134/JKMS.2005.42.3.447
  6. B.-Y. Chen & P. Piccinni: Submanifolds with finite type Gauss map. Bull. Austral. Math. Soc. 35 (1987), 161-186. https://doi.org/10.1017/S0004972700013162
  7. U. Dursun: Flat surfaces in the Euclidean space $E^3$ with pointwise 1-type Gauss map. Bull. Malays. Math. Sci. Soc.(2) 33 (2010), no. 3, 469-478.
  8. D.-S. Kim & Y.H. Kim: Surfaces with planar lines of curvature. Honam Math. J. 32 (2010), 777-790. https://doi.org/10.5831/HMJ.2010.32.4.777
  9. Y.H. Kim & D.W. Yoon: Ruled surfaces with finite type Gauss map in Minkowski spaces. Soochow J. Math. 26 (2000), 85-96.
  10. J. Oprea: Differential geometry and its applications. Prentice Hall, New Jersey, 1997.

피인용 문헌

  1. ON THE GAUSS MAP OF GENERALIZED SLANT CYLINDRICAL SURFACES vol.20, pp.3, 2011, https://doi.org/10.7468/jksmeb.2013.20.3.149