Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On linear Weingarten surfaces   In this paper we study surfaces in Euclidean 3-space that satisfy a
Weingarten condition of linear type as $\kappa_1=m \kappa_2 +n$, where $m$ and
$n$ are real numbers and $\kappa_1$ and $\kappa_2$ denote the principal
curvatures at each point of the surface. We investigate the possible existence
of such surfaces parametrized by a uniparametric family of circles. Besides the
surfaces of revolution, we prove that not exist more except the case
$(m,n)=(-1,0)$, that is, if the surface is one of the classical examples of
minimal surfaces discovered by Riemann.

34
The categories of this paper are: chem-ph
24
The categories of this paper are: dg-ga
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
3
The categories of this paper are: physics
30
The categories of this paper are: q-alg
26
The categories of this paper are: bayes-an
10
The categories of this paper are: q-bio
5
The categories of this paper are: gr-qc
14
The categories of this paper are: math-ph
9
The categories of this paper are: nlin
18
The categories of this paper are: econ
16
The categories of this paper are: stat
17
The categories of this paper are: q-fin
0
The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci