On the uniqueness of complete biconservative surfaces in ℝ³

Nistor, Simona; Oniciuc, Cezar

doi:10.1090/proc/14322

On the uniqueness of complete biconservative surfaces in $\mathbb {R}^3$
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by Simona Nistor and Cezar Oniciuc

Proc. Amer. Math. Soc. 147 (2019), 1231-1245

DOI: https://doi.org/10.1090/proc/14322

Published electronically: November 16, 2018

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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.

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