Cheng-Yau operator and Gauss map of Translation Surfaces

한국수학교육학회지시리즈B:순수및응용수학 / 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 (Department of Mathematics, Chonnam National University)
Kim, Dong-Soo (Department of Mathematics, Chonnam National University)

Kim, Dong Seo, & Kim, Dong-Soo. (2021). CHENG -YAU OPERATOR AND GAUSS MAP OF TRANSLATION SURFACES. 한국수학교육학회지시리즈B:순수및응용수학, 28(1), 43-53, https://doi.org/https://doi.org/10.7468/jksmeb.2021.28.1.43

복사

Abstract

We study translation surfaces in the Euclidean 3-space &#55349;&#56636;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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논문 상세

Vol.28 No.1

CHENG -YAU OPERATOR AND GAUSS MAP OF TRANSLATION SURFACES

Cheng-Yau operator and Gauss map of Translation Surfaces

Abstract

한국수학교육학회지시리즈B:순수및응용수학