On the uniqueness of complete biconservative surfaces in $\mathbb{R}^3$

Simona Nistor; Cezar Oniciuc

On the uniqueness of complete biconservative surfaces in $\mathbb{R}^3$

Differential Geometry 2017-11-21 v1 General Topology

Authors: Simona Nistor , Cezar Oniciuc

Abstract

We study the uniqueness of complete biconservative surfaces in the Euclidean space $\mathbb{R}^3$ , and prove that the only complete biconservative regular surfaces in $\mathbb{R}^3$ are either $CMC$ or certain surfaces of revolution. In particular, any compact biconservative regular surface in $\mathbb{R}^3$ is a round sphere.

Keywords

biconservative surfaces complete surfaces uniqueness euclidean space constant mean curvature surfaces of revolution

Cite

@article{arxiv.1711.07253,
  title  = {On the uniqueness of complete biconservative surfaces in $\mathbb{R}^3$},
  author = {Simona Nistor and Cezar Oniciuc},
  journal= {arXiv preprint arXiv:1711.07253},
  year   = {2017}
}

Comments

15 pages, 2 figures

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