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arXiv · 1905.00962

Characterization of quadric surfaces in terms of coordinate finite type Gauss map

Mutaz Al-Sabbagh·Hassan Al-Zoubi
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Abstract

In this article, we introduce an important class of surfaces, namely, quadrics in the Euclidean 3-space $\mathbb{E}^{3}$. We prove that planes, spheres and circular cylinders are the only quadric surfaces whose Gauss map $\boldsymbol{G}$ satisfies a relation of the form $\Delta^{I}\boldsymbol{G}= M \boldsymbol{G}$, where $M$ is a square matrix of order 3 and $\Delta^{I}$ is the Laplace-Beltrami operator corresponding to the first fundamental form $I$ of the surface.

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Mutaz Al-Sabbagh, Hassan Al-Zoubi. 2019-04-29. Characterization of quadric surfaces in terms of coordinate finite type Gauss map. https://arxiv.org/abs/1905.00962

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