On the Gauss map of surfaces of revolution without parabolic points
Bull. Korean Math. Soc. 2009 Vol. 46, No. 6, 1141-1149
https://doi.org/10.4134/BKMS.2009.46.6.1141
Published online November 1, 2009
Young Ho Kim, Chul Woo Lee, and Dae Won Yoon
Kyungpook National University, Kyungpook National University, and Gyeongsang National University
Abstract : In this article, we study surfaces of revolution without parabolic points in a Euclidean 3-space whose Gauss map $G$ satisfies the condition $\Delta^h G = A G,A\in \text{Mat}(3,\Bbb R)$, where $\Delta^h $ denotes the Laplace operator of the second fundamental form $h$ of the surface and $\text{Mat}(3,\Bbb R)$ 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
MSC numbers : 53A05, 53B25
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