Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A symmetric 2-tensor canonically associated to Q-curvature and its
  applications   In this article, we define a symmetric 2-tensor canonically associated to
Q-curvature called J-tensor on any Riemannian manifold with dimension at least
three. The relation between J-tensor and Q-curvature is precisely like Ricci
tensor and scalar curvature. Thus it can be interpreted as a higher-order
analogue of Ricci tensor. This tensor can also be used to understand
Chang-Gursky-Yang's theorem on 4-dimensional Q-singular metrics. Moreover, we
show an Almost-Schur Lemma holds for Q-curvature, which gives an estimate of
Q-curvature on closed manifolds.

28
The categories of this paper are: alg-geom
25
The categories of this paper are: patt-sol
17
The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
35
The categories of this paper are: mtrl-th
13
The categories of this paper are: quant-ph
10
The categories of this paper are: q-bio
9
The categories of this paper are: nlin
26
The categories of this paper are: bayes-an
11
The categories of this paper are: hep-lat
36
The categories of this paper are: cmp-lg
6
The categories of this paper are: astro-ph
24
The categories of this paper are: dg-ga
12
The categories of this paper are: nucl-th
5
The categories of this paper are: gr-qc
3
The categories of this paper are: physics