Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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HELICOIDAL SURFACES WITH POINTWISE 1-TYPE GAUSS MAP

  • Choi, Mie-Kyung (DEPARTMENT OF MATHEMATICS CHONNAM NATIONAL UNIVERSITY) ;
  • Kim, Dong-Soo (DEPARTMENT OF MATHEMATICS CHONNAM NATIONAL UNIVERSITY) ;
  • Kim, Young-Ho (DEPARTMENT OF MATHEMATICS KYUNGPOOK NATIONAL UNIVERSITY)
  • Published : 2009.01.31
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Abstract

The helicoidal surfaces with pointwise 1-type or harmonic gauss map in Euclidean 3-space are studied. The notion of pointwise 1-type Gauss map is a generalization of usual sense of 1-type Gauss map. In particular, we prove that an ordinary helicoid is the only genuine helicoidal surface of polynomial kind with pointwise 1-type Gauss map of the first kind and a right cone is the only rational helicoidal surface with pointwise 1-type Gauss map of the second kind. Also, we give a characterization of rational helicoidal surface with harmonic or pointwise 1-type Gauss map.

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References

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