ON THE GAUSS MAP OF SURFACES OF REVOLUTION WITHOUT PARABOLIC POINTS

Kim, Young-Ho; Lee, Chul-Woo; Yoon, Dae-Won

doi:10.4134/BKMS.2009.46.6.1141

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ON THE GAUSS MAP OF SURFACES OF REVOLUTION WITHOUT PARABOLIC POINTS

Journal title : Bulletin of the Korean Mathematical Society
Volume 46, Issue 6, 2009, pp.1141-1149
Publisher : The Korean Mathematical Society
DOI : 10.4134/BKMS.2009.46.6.1141

Title & Authors

ON THE GAUSS MAP OF SURFACES OF REVOLUTION WITHOUT PARABOLIC POINTS
Kim, Young-Ho; Lee, Chul-Woo; Yoon, Dae-Won;

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.

Keywords

Gauss map;surface of revolution;Laplace operator;second fundamental form;

Language

English

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