CMC biconservative surfaces in $\mathbb{S}^n\times\mathbb{R}$ and $\mathbb{H}^n\times\mathbb{R}$

Dorel Fetcu; Cezar Oniciuc; Ana Lucia Pinheiro

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arXiv · 1408.5437

CMC biconservative surfaces in $\mathbb{S}^n\times\mathbb{R}$ and $\mathbb{H}^n\times\mathbb{R}$

Dorel Fetcu·Cezar Oniciuc·Ana Lucia Pinheiro

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Abstract

We classify non-minimal biconservative surfaces with parallel mean curvature vector field in $\mathbb{S}^n\times\mathbb{R}$ and $\mathbb{H}^n\times\mathbb{R}$. When these surfaces do not lie in $\mathbb{S}^n$ or $\mathbb{H}^n$ and they are not vertical cylinders, we find their explicit (local) equation. We also prove a result on the compactness of biconservative surfaces with constant mean curvature in Hadamard manifolds.

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Dorel Fetcu, Cezar Oniciuc, Ana Lucia Pinheiro. 2014-08-22. CMC biconservative surfaces in $\mathbb{S}^n\times\mathbb{R}$ and $\mathbb{H}^n\times\mathbb{R}$. https://arxiv.org/abs/1408.5437

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