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http://dx.doi.org/10.7468/jksmeb.2021.28.1.43

CHENG -YAU OPERATOR AND GAUSS MAP OF TRANSLATION SURFACES  

Kim, Dong Seo (Department of Mathematics, Chonnam National University)
Kim, Dong-Soo (Department of Mathematics, Chonnam National University)
Publication Information
The Pure and Applied Mathematics / v.28, no.1, 2021 , pp. 43-53 More about this Journal
Abstract
We study translation surfaces in the Euclidean 3-space ��3 and the Gauss map N with respect to the so-called Cheng-Yau operator ☐. As a result, we prove that the only translation surfaces with Gauss map N satisfying ☐N = AN for some 3 × 3 matrix A are the flat ones. We also show that the only translation surfaces with Gauss map N satisfying ☐N = AN for some nonzero 3 × 3 matrix A are the cylindrical surfaces.
Keywords
Gauss map; Cheng -Yau operator; translation surface; Gaussian curvature; mean curvature;
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Times Cited By KSCI : 1  (Citation Analysis)
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