Bulletin of the
Korean Mathematical Society BKMS

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