Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Classes of Weingarten Surfaces in S^2xR   In this work we study surfaces in radial conformally flat spaces. We
characterize surfaces of rotation with constant Gaussian and Extrinsic
curvature in these radial 3-spaces. We prove that all the spheres in the
conformal 3-space have constant Gaussian curvature $K=1$ if, and only if, the
conformal factor is special. In this special case we study geometric properties
of this ambient 3-space, and as an application we prove that it is isometric to
the space ${\mathbb{S}}^2\times {\mathbb{R}}$, so we consider it as the {\em
Radial Model} of ${\mathbb{S}}^2\times {\mathbb{R}}$. We obtain two classes of
Weingarten surfaces in the {\em Radial Model}, which satisfy
$\tilde{K}_E+\tilde{H}^2-\tilde{K}=0 $ and $2\tilde{K}_E-\tilde{K}=0 $, where
$\tilde{K}$ is the Gaussian curvature, $\tilde{H}$ is the mean curvature and
$\tilde{K}_E$ is the extrinsic curvature. Moreover, by using the relations
between the curvatures of the {\em Radial Model} and the curvatures with
respect to the euclidean metric ([CPS]), we prove that first class the
Weingarten surfaces in {\em Radial Model} corresponds, up to isometries, to the
minimal surfaces in $\mathbb{R}^3$, and second class corresponds to EDSGHW -
surfaces in Euclidean space $ \mathbb{R} ^ 3$(\cite{DC}). Consequently these
two classes of surfaces have a Weierstrass type representation depending on two
holomorphic functions.

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The categories of this paper are: atom-ph
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The categories of this paper are: funct-an
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The categories of this paper are: cond-mat
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The categories of this paper are: q-fin
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The categories of this paper are: adap-org
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-ph
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The categories of this paper are: q-alg
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The categories of this paper are: math-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: physics
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The categories of this paper are: gr-qc
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The categories of this paper are: stat
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The categories of this paper are: solv-int
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The categories of this paper are: bayes-an
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The categories of this paper are: econ