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2001•Bulletin of the Korean Mathematical SocietyRequires access

CHARACTERIZATION OF THE HELICOID AS RULED SURFACES WITH POINTWISE 1-TYPE GAUSS MAP

Miekyung Choi, Young Ho Kim

Open publisher page 78 citations

Abstract

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.

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What this paper is about

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.

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OpenAlex reports 78 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

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.

Key concepts: Helicoid, Pointwise, Gauss map, Mathematics, Type (biology), Characterization (materials science), Gauss, Pure mathematics

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