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http://dx.doi.org/10.4134/JKMS.2009.46.1.215

HELICOIDAL SURFACES WITH POINTWISE 1-TYPE GAUSS MAP  

Choi, Mie-Kyung (DEPARTMENT OF MATHEMATICS CHONNAM NATIONAL UNIVERSITY)
Kim, Dong-Soo (DEPARTMENT OF MATHEMATICS CHONNAM NATIONAL UNIVERSITY)
Kim, Young-Ho (DEPARTMENT OF MATHEMATICS KYUNGPOOK NATIONAL UNIVERSITY)
Publication Information
Journal of the Korean Mathematical Society / v.46, no.1, 2009 , pp. 215-223 More about this Journal
Abstract
The helicoidal surfaces with pointwise 1-type or harmonic gauss map in Euclidean 3-space are studied. The notion of pointwise 1-type Gauss map is a generalization of usual sense of 1-type Gauss map. In particular, we prove that an ordinary helicoid is the only genuine helicoidal surface of polynomial kind with pointwise 1-type Gauss map of the first kind and a right cone is the only rational helicoidal surface with pointwise 1-type Gauss map of the second kind. Also, we give a characterization of rational helicoidal surface with harmonic or pointwise 1-type Gauss map.
Keywords
helicoidal surfaces; helicoid; right cone; pointwise 1-type Gauss map;
Citations & Related Records
Times Cited By KSCI : 2  (Citation Analysis)
Times Cited By Web Of Science : 2  (Related Records In Web of Science)
Times Cited By SCOPUS : 2
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