Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A variational characterization of flat spaces in dimension three   In this short note we prove that, in dimension three, flat metrics are the
only complete metrics with non-negative scalar curvature which are critical for
the $\sigma_{2}$-curvature functional.

27
The categories of this paper are: comp-gas
21
The categories of this paper are: adap-org
8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph
19
The categories of this paper are: eess
33
The categories of this paper are: plasm-ph
25
The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th
12
The categories of this paper are: nucl-th
13
The categories of this paper are: quant-ph
17
The categories of this paper are: q-fin
9
The categories of this paper are: nlin
4
The categories of this paper are: cond-mat
23
The categories of this paper are: solv-int
20
The categories of this paper are: acc-phys