Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Weingarten type surfaces in $\mathbb{H}^2\times\mathbb{R}$ and
  $\mathbb{S}^2\times\mathbb{R}$   In this article, we study complete surfaces $\Sigma$, isometrically immersed
in the product space $\mathbb{H}^2\times\mathbb{R}$ or
$\mathbb{S}^2\times\mathbb{R}$ having positive extrinsic curvature $K_e$. Let
$K_i$ denote the intrinsic curvature of $\Sigma$. Assume that the equation
$aK_i+bK_e=c$ holds for some real constants $a\neq0$, $b>0$ and $c$. The main
result of this article state that when such a surface is a topological sphere
it is rotational.

6
The categories of this paper are: astro-ph
27
The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
34
The categories of this paper are: chem-ph
17
The categories of this paper are: q-fin
20
The categories of this paper are: acc-phys
1
The categories of this paper are: cs
14
The categories of this paper are: math-ph
15
The categories of this paper are: nucl-ex
23
The categories of this paper are: solv-int
24
The categories of this paper are: dg-ga
16
The categories of this paper are: stat
21
The categories of this paper are: adap-org
5
The categories of this paper are: gr-qc
8
The categories of this paper are: hep-ex