Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Some positivity results of the curvature on the group corresponding to
  the incompressible Euler equation with Coriolis force   In this article, we investigate the geometry of a central extension
$\widehat{\mathcal D}_{\mu}(S^{2})$ of the group of volume-preserving
diffeomorphisms of the 2-sphere equipped with the $L^{2}$-metric, whose
geodesics correspond solutions of the incompressible Euler equation with
Coriolis force. In particular, we calculate the Misiolek curvature of this
group. This value is related to the existence of a conjugate point and its
positivity directly implies the positivity of the sectional curvature.

13
The categories of this paper are: quant-ph
9
The categories of this paper are: nlin
26
The categories of this paper are: bayes-an
1
The categories of this paper are: cs
17
The categories of this paper are: q-fin
15
The categories of this paper are: nucl-ex
14
The categories of this paper are: math-ph
18
The categories of this paper are: econ
5
The categories of this paper are: gr-qc
24
The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
29
The categories of this paper are: funct-an
30
The categories of this paper are: q-alg
21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat
8
The categories of this paper are: hep-ex