Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Surfaces with parallel mean curvature in $\mathbb{S}^3\times\mathbb{R}$
  and $\mathbb{H}^3\times\mathbb{R}$   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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The categories of this paper are: eess
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The categories of this paper are: patt-sol
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-th
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-ex
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The categories of this paper are: quant-ph
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The categories of this paper are: funct-an
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The categories of this paper are: acc-phys
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The categories of this paper are: adap-org
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The categories of this paper are: astro-ph
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The categories of this paper are: nlin
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The categories of this paper are: alg-geom
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The categories of this paper are: solv-int
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The categories of this paper are: cond-mat