Surfaces with parallel mean curvature in $\mathbb{S}^3\times\mathbb{R}$ and $\mathbb{H}^3\times\mathbb{R}$

preprint2011arXivOpen access

We prove a Simons type equation for non-minimal surfaces with parallel mean curvature vector (pmc surfaces) in $M^3(c)\times\mathbb{R}$ , where $M^3(c)$ is a 3-dimensional space form. Then, we use this equation in order to characterize certain complete non-minimal pmc surfaces.

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Surfaces with parallel mean curvature in $\mathbb{S}^3\times\mathbb{R}$ and $\mathbb{H}^3\times\mathbb{R}$

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Surfaces with parallel mean curvature in S3×R\mathbb{S}^3\times\mathbb{R}S3×R and H3×R\mathbb{H}^3\times\mathbb{R}H3×R

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Surfaces with parallel mean curvature in $\mathbb{S}^3\times\mathbb{R}$ and $\mathbb{H}^3\times\mathbb{R}$