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Bull. Korean Math. Soc. 2001; 38(4): 753-761
Printed December 1, 2001
Copyright © The Korean Mathematical Society.
Characterization of the helicoid as ruled surfaces with pointwise 1-type Gauss map
Miekyung Choi and Young Ho Kim
Kyungpook National University, Kyungpook National University
We introduce the notion of Gauss map of pointwise 1-type on ruled surfaces in the Euclidean 3-space for which vector valued functions is neither trivial nor it extends or coincides with the usual notion of 1-type, in general. We characterize the minimal helicoid in terms of it and give a complete classification of the ruled surfaces with pointwise 1-type Gauss map.
Keywords: helicoid, Gauss map, ruled surface, pointwise 1-type
MSC numbers: 53B25, 53C40
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