Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Curvature computations for a two-component Camassa-Holm equation with
  vorticity   In the present paper, a two-component Camassa-Holm (2CH) system with
vorticity is studied as a geodesic flow on a suitable Lie group. The paper aims
at presenting various details of the geometric formalism and a major result is
the computation of the sectional curvature $K$ of the underlying configuration
manifold. As a further result, we show that there are directions for which $K$
is strictly positive and bounded away from zero.

31
The categories of this paper are: ao-sci
19
The categories of this paper are: eess
10
The categories of this paper are: q-bio
7
The categories of this paper are: hep-th
23
The categories of this paper are: solv-int
14
The categories of this paper are: math-ph
5
The categories of this paper are: gr-qc
22
The categories of this paper are: chao-dyn
37
The categories of this paper are: supr-con
21
The categories of this paper are: adap-org
11
The categories of this paper are: hep-lat
13
The categories of this paper are: quant-ph
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
32
The categories of this paper are: atom-ph
12
The categories of this paper are: nucl-th