English

On regular algebraic surfaces of $R^3$ with constant mean curvature

Differential Geometry 2014-03-28 v1

Abstract

We consider regular surfaces MM that are given as the zeros of a polynomial function p:R3Rp:R^3\rightarrow R, where the gradient of pp vanishes nowhere. We assume that MM has non-zero mean curvature and prove that there exist only two examples of such surfaces, namely the sphere and the circular cylinder.

Keywords

Cite

@article{arxiv.1403.7029,
  title  = {On regular algebraic surfaces of $R^3$ with constant mean curvature},
  author = {João Lucas Marques Barbosa and Manfredo Perdigão do Carmo},
  journal= {arXiv preprint arXiv:1403.7029},
  year   = {2014}
}