## arXiv Analytics

### arXiv:1711.07253 [math.DG]AbstractReferencesReviewsResources

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

Published 2017-11-20Version 1

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.

Complete biconservative surfaces in $\mathbb{R}^3$ and $\mathbb{S}^3$
The construction of complete biconservative surfaces in $\mathbb{S}^3$
Complete biconservative surfaces in the hyperbolic space $\mathbb{H}^3$