English

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

Differential Geometry 2011-06-22 v1

Abstract

In the present paper we classify all surfaces in \E3\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 E3{\mathbb{E}}^3 is the catenoid.

Keywords

Cite

@article{arxiv.1004.4255,
  title  = {On certain surfaces in the Euclidean space ${\mathbb{E}}^3$},
  author = {Marian Ioan Munteanu and Ana Irina Nistor},
  journal= {arXiv preprint arXiv:1004.4255},
  year   = {2011}
}

Comments

13 Latex pages

R2 v1 2026-06-21T15:14:18.083Z