In the present paper we classify all surfaces in 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 3 is the catenoid.
@article{bwmeta1.element.doi-10_2478_s11533-011-0001-7,
author = {Marian Munteanu and Ana Nistor},
title = {Complete classification of surfaces with a canonical principal direction in the Euclidean space \[ \mathbb {E} \]
3},
journal = {Open Mathematics},
volume = {9},
year = {2011},
pages = {378-389},
zbl = {1222.53009},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-011-0001-7}
}
Marian Munteanu; Ana Nistor. Complete classification of surfaces with a canonical principal direction in the Euclidean space \[ \mathbb {E} \]
3. Open Mathematics, Tome 9 (2011) pp. 378-389. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-011-0001-7/
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