RULED SURFACES AND GAUSS MAP

We study the Gauss map G of ruled surfaces in the 3-dim- ensional 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 ruled surfaces with Gauss map G satisfying □G =...

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Published in:Taehan Suhakhoe hoebo 2015, 52(5), , pp.1661-1668
Main Author: KIM, DONG-SOO
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description We study the Gauss map G of ruled surfaces in the 3-dim- ensional 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 ruled surfaces with Gauss map G satisfying □G = AG for some 3 × 3 matrix A are the flat ones. Furthermore, we show that the only ruled surfaces with Gauss map G satisfying □G = AG for some nonzero 3×3 matrix A are the cylindrical surfaces. KCI Citation Count: 1
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title RULED SURFACES AND GAUSS MAP
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