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arxiv: 1102.0219 · v2 · pith:52ITQ73Onew · submitted 2011-02-01 · 🧮 math.DG

A Simons type formula for surfaces with parallel mean curvature

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

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