Complete classification of surfaces with a canonical principal direction in the Euclidean space
\mathbb{E}
3 |
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| Authors: | Marian Ioan Munteanu Ana Irina Nistor |
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| Institution: | 1. Faculty of Mathematics, Alexandru Ioan Cuza University of Ia?i, Ia?i, Romania
2. Departement Wiskunde, Katholieke Universiteit Leuven, Leuven, Belgium
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| Abstract: | In the present paper we classify all surfaces in $
\mathbb{E}
$
\mathbb{E}
3 with a canonical principal direction. Examples of this type of surfaces are constructed. We prove that the only minimal surface
with a canonical principal direction in the Euclidean space $
\mathbb{E}
$
\mathbb{E}
3 is the catenoid. |
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| Keywords: | |
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