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

Simona Nistor, Cezar Oniciuc

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.