Taiwanese Journal of Mathematics

CLASSIFICATION OF RULED SURFACES WITH POINTWISE 1-TYPE GAUSS MAP

Miekyung Choi, Young Ho Kim, and Dae Won Yoon

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Abstract

Ruled surfaces with the Gauss map satisfying a partial differential equation which is similar to an eigenvalue problem in a 3-dimensional Euclidean space are studied. Such a Gauss map is said to be of pointwise 1-type, namely, the Gauss map $G$ satisfies $\Delta G = f(G+C)$, where $\Delta$ is the Laplacian operator, $f$ is a non-zero function and $C$ is a constant vector. As a result, such ruled surfaces are completely determined by the function $f$ and the vector $C$ when their Gauss map is of pointwise 1-type. New examples of ruled surfaces called cylinders of an infinite type and rotational ruled surfaces are introduced in this regard.

Article information

Source
Taiwanese J. Math., Volume 14, Number 4 (2010), 1297-1308.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500405946

Digital Object Identifier
doi:10.11650/twjm/1500405946

Mathematical Reviews number (MathSciNet)
MR2663912

Zentralblatt MATH identifier
1215.53022

Subjects
Primary: 53B25: Local submanifolds [See also 53C40] 53C40: Global submanifolds [See also 53B25]

Keywords
ruled surface Gauss map pointwise 1-type cylinder of an infinite type rotational ruled surface

Citation

Choi, Miekyung; Kim, Young Ho; Yoon, Dae Won. CLASSIFICATION OF RULED SURFACES WITH POINTWISE 1-TYPE GAUSS MAP. Taiwanese J. Math. 14 (2010), no. 4, 1297--1308. doi:10.11650/twjm/1500405946. https://projecteuclid.org/euclid.twjm/1500405946


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