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

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

2010-04-24

arxiv.org/abs/1004.4255v1

Central European Journal of Mathematics,9 (2011) 2, 378 - 389

Mathematics

Differential Geometry

13 Latex pages

Scientific paper

10.2478/s11533-011-0001-7

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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