Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The space of associated metrics on a symplectic manifold   The spaces of Riemannian metrics on a closed manifold $M$ are studied. On the
space ${\mathcal M}$ of all Riemannian metrics on $M$ the various weak
Riemannian structures are defined and the corresponding connections are
studied. The space ${\mathcal AM}$ of associated metrics on a symplectic
manifold $M,\omega$ is considered in more detail. A natural parametrization of
the space ${\mathcal AM}$ is defined. It is shown, that ${\mathcal AM}$ is a
complex manifold. A curvature of the space ${\mathcal AM}$ and quotient space
${\mathcal AM}/{\mathcal D}_{\omega}$ is found. The finite dimensionality of
the space of associated metrics of a constant scalar curvature with Hermitian
Ricci tensor is shown.

6
The categories of this paper are: astro-ph
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph
11
The categories of this paper are: hep-lat
27
The categories of this paper are: comp-gas
1
The categories of this paper are: cs
34
The categories of this paper are: chem-ph
26
The categories of this paper are: bayes-an
24
The categories of this paper are: dg-ga
13
The categories of this paper are: quant-ph
4
The categories of this paper are: cond-mat
22
The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc