The Pure and Applied Mathematics (한국수학교육학회지시리즈B:순수및응용수학)

Korean Society of Mathematical Education (한국수학교육학회)
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ON THE GAUSS MAP OF GENERALIZED SLANT CYLINDRICAL SURFACES

  • Kim, Dong-Soo (Department of Mathematics, Chonnam National University) ;
  • Song, Booseon (Department of Mathematics, Chonnam National University)
  • Received : 2013.01.19
  • Accepted : 2013.05.21
  • Published : 2013.08.31
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Abstract

In this article, we study the Gauss map of generalized slant cylindrical surfaces (GSCS's) in the 3-dimensional Euclidean space $\mathbb{E}^3$. 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 ${\Delta}G=AG$ for some $3{\times}3$ matrix A are the planes, the spheres and the circular cylinders.

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References

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