Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: Some rigidity characterizations on critical metrics for quadratic
  curvature functionals
12
The categories of this paper are: nucl-th
29
The categories of this paper are: funct-an
21
The categories of this paper are: adap-org
31
The categories of this paper are: ao-sci
30
The categories of this paper are: q-alg
28
The categories of this paper are: alg-geom
26
The categories of this paper are: bayes-an
4
The categories of this paper are: cond-mat
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
8
The categories of this paper are: hep-ex
14
The categories of this paper are: math-ph
3
The categories of this paper are: physics
9
The categories of this paper are: nlin
5
The categories of this paper are: gr-qc
22
The categories of this paper are: chao-dyn