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

Dorel Fetcu; Harold Rosenberg

arxiv: 1103.6254 · v1 · pith:JGFKKGWCnew · submitted 2011-03-31 · 🧮 math.DG

Surfaces with parallel mean curvature in mathbb{S}³timesmathbb{R} and mathbb{H}³timesmathbb{R}

Dorel Fetcu , Harold Rosenberg This is my paper

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keywords mathbbsurfacestimescurvatureequationmeannon-minimalparallel

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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}³timesmathbb{R} and mathbb{H}³timesmathbb{R}

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