Cheng–Yau Operator and Gauss Map of Surfaces of Revolution

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• 作者：Dong-Soo Kim ; Jong Ryul Kim ; Young Ho Kim
• 关键词：Gauss map ; Cheng–Yau operator ; Surfaces of revolution
• 刊名：Bulletin of the Malaysian Mathematical Sciences Society
• 出版年：2016
• 出版时间：October 2016
• 年：2016
• 卷：39
• 期：4
• 页码：1319-1327
• 全文大小：430 KB
• 刊物类别：Mathematics, general; Applications of Mathematics;
• 刊物主题：Mathematics, general; Applications of Mathematics;
• 出版者：Springer Singapore
• ISSN：2180-4206
• 卷排序：39

文摘

We study the Gauss map G of surfaces of revolution in the 3-dimensional Euclidean space \({{\mathbb {E}}^3}\) with respect to the so-called Cheng–Yau operator \(\square \) acting on the functions defined on the surfaces. As a result, we establish the classification theorem that the only surfaces of revolution with Gauss map G satisfying \(\square G=AG\) for some \(3\times 3\) matrix A are the planes, right circular cones, circular cylinders, and spheres.