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

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

2011-03-31

arxiv.org/abs/1103.6254v1

Mathematics

Differential Geometry

13 pages

Scientific paper

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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