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Bull. Korean Math. Soc. 2013; 50(4): 1345-1356

Printed July 1, 2013

https://doi.org/10.4134/BKMS.2013.50.4.1345

Copyright © The Korean Mathematical Society.

Classifications of helicoidal surfaces with $L_1$-pointwise 1-type Gauss map

Young Ho Kim and Nurettin Cenk Turgay

Kyungpook National University, Istanbul Technical University

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In this paper, we study rotational and helicoidal surfaces in Euclidean 3-space in terms of their Gauss map. We obtain a complete classification of these type of surfaces whose Gauss maps $G$ satisfy $L_1 G=f(G+C)$ for some constant vector $C\in\mathbb E^3$ and smooth function $f$, where $L_1$ denotes the Cheng-Yau operator.

Keywords: Gauss map, $L_1$-pointwise 1-type, Cheng-Yau operator, rotational surface, helicoidal surface, Lie point symmetry

MSC numbers: 53B25, 53C40

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