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

Simona Nistor; Cezar Oniciuc

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arXiv · 1711.07253

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

Simona Nistor·Cezar Oniciuc

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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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BibTeX RIS

Simona Nistor, Cezar Oniciuc. 2017-11-20. On the uniqueness of complete biconservative surfaces in $\mathbb{R}^3$. https://arxiv.org/abs/1711.07253

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