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ISSN : 1226-0657

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Vol.20 No.3
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ON THE GAUSS MAP OF GENERALIZED SLANT CYLINDRICAL SURFACES

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081
2013, v.20 no.3, pp.149-158
https://doi.org/10.7468/jksmeb.2013.20.3.149
Kim, Dong-Soo
Song, Booseon
Kim,, D. , & Song,, B. (2013). ON THE GAUSS MAP OF GENERALIZED SLANT CYLINDRICAL SURFACES. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 20(3), 149-158, https://doi.org/10.7468/jksmeb.2013.20.3.149
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Abstract

In this article, we study the Gauss map of generalized slant cylindrical surfaces (GSCS's) in the 3-dimensional Euclidean space <TEX>$\mathbb{E}^3$</TEX>. Surfaces of revolution, cylindrical surfaces and tubes along a plane curve are special cases of GSCS's. Our main results state that the only GSCS's with Gauss map G satisfying <TEX>${\Delta}G=AG$</TEX> for some <TEX>$3{\times}3$</TEX> matrix A are the planes, the spheres and the circular cylinders.

keywords
Gauss map, Laplace operator, surface of rotation, cylindrical surface, slant cylindrical surface, generalized slant cylindrical surface

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Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics

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