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

Dorel Fetcu; Cezar Oniciuc; Ana Lucia Pinheiro

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

Differential Geometry 2014-08-26 v1

Authors: Dorel Fetcu , Cezar Oniciuc , Ana Lucia Pinheiro

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.

Keywords

biconservative surfaces constant mean curvature parallel mean curvature vector $\mathbb{S}^n\times\mathbb{R}$ $\mathbb{H}^n\times\mathbb{R}$ Hadamard manifolds

Cite

@article{arxiv.1408.5437,
  title  = {CMC biconservative surfaces in $\mathbb{S}^n\times\mathbb{R}$ and $\mathbb{H}^n\times\mathbb{R}$},
  author = {Dorel Fetcu and Cezar Oniciuc and Ana Lucia Pinheiro},
  journal= {arXiv preprint arXiv:1408.5437},
  year   = {2014}
}

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19 pages

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