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ON THE GAUSS MAP OF SURFACES OF REVOLUTION WITHOUT PARABOLIC POINTS

  • Kim, Young-Ho (Department of Mathematics Teachers' College Kyungpook National University) ;
  • Lee, Chul-Woo (Department of Mathematics College of Natural Sciences Kyungpook National University) ;
  • Yoon, Dae-Won (Department of Mathematics Education and RINS Gyeongsang National University)
  • Published : 2009.11.30

Abstract

In this article, we study surfaces of revolution without parabolic points in a Euclidean 3-space whose Gauss map G satisfies the condition ${\Delta}^hG\;=\;AG,A\;{\in}\;Mat(3,{\mathbb{R}}),\;where\;{\Delta}^h$ denotes the Laplace operator of the second fundamental form h of the surface and Mat(3,$\mathbb{R}$) the set of 3${\times}$3-real matrices, and also obtain the complete classification theorem for those. In particular, we have a characterization of an ordinary sphere in terms of it.

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  3. Classification of rotational surfaces in pseudo-Galilean space vol.50, pp.2, 2015, https://doi.org/10.3336/gm.50.2.13
  4. SURFACES OF REVOLUTION WITH LIGHT-LIKE AXIS vol.25, pp.4, 2012, https://doi.org/10.14403/jcms.2012.25.4.677