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arXiv · 1004.4255

On certain surfaces in the Euclidean space ${\mathbb{E}}^3$

Marian Ioan Munteanu·Ana Irina Nistor
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Abstract

In the present paper we classify all surfaces in $\E^3$ with a canonical principal direction. Examples of these type of surfaces are constructed. We prove that the only minimal surface with a canonical principal direction in the Euclidean space ${\mathbb{E}}^3$ is the catenoid.

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Marian Ioan Munteanu, Ana Irina Nistor. 2010-04-24. On certain surfaces in the Euclidean space ${\mathbb{E}}^3$. https://doi.org/10.2478/s11533-011-0001-7

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