Cheng–Yau Operator and Gauss Map of Surfaces of Revolution

• DOI: 10.1007/s40840-015-0234-x
• Publication Date: 2015-09-29T09:41:28Z
• Authors: Dong-Soo Kim; Jong Ryul Kim; Young Ho Kim
• Keywords: Gauss map; Surface of revolution; Square (algebra); Operator (biology); Matrix (chemical analysis)

14pages<br/>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 $3\times3$ matrix $A$ are the planes, right circular cones, circular cylinders and spheres.<br/>