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  • P-ISSN1226-0657
  • E-ISSN2287-6081
  • KCI

ISSN : 1226-0657

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Vol.28 No.1

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Cheng-Yau operator and Gauss map of Translation Surfaces

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081
2021, v.28 no.1, pp.43-53
https://doi.org/https://doi.org/10.7468/jksmeb.2021.28.1.43
Kim, Dong Seo
Kim, Dong-Soo
Kim,, D. S. , & Kim,, D. (2021). Cheng-Yau operator and Gauss map of Translation Surfaces. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 28(1), 43-53, https://doi.org/https://doi.org/10.7468/jksmeb.2021.28.1.43

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

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics

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