Cheng-Yau operator and Gauss map of surfaces of revolution
Abstract
We study the Gauss map G of surfaces of revolution in the 3-dimensional Euclidean space E3 with respect to the so called Cheng-Yau operator 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 G=AG for some 3×3 matrix A are the planes, right circular cones, circular cylinders and spheres.
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