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Commun. Korean Math. Soc. 2017; 32(3): 715-724
Online first article March 28, 2017 Printed July 31, 2017
https://doi.org/10.4134/CKMS.c160188
Copyright © The Korean Mathematical Society.
On the Gauss map of helicoidal surfaces
Dong-Soo Kim, Wonyong Kim, and Young Ho Kim
Chonnam National University, Chonnam National University, Kyungpook National University
We study the Gauss map $G$ of helicoidal surfaces in the 3-dimensional Euclidean space ${\mathbb{E}^3}$ with respect to the so called Cheng-Yau operator $\square$ acting on the functions defined on the surfaces. As a result, we completely classify the helicoidal surfaces with Gauss map $G$ satisfying $\square G=AG$ for some $3\times3$ matrix $A$.
Keywords: Gauss map, helicoidal surfaces, Laplace operator, Cheng-Yau operator
MSC numbers: 53A05, 53B25
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