Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Einstein-type structures, Besse's conjecture and a uniqueness result for
  a $\varphi$-CPE metric in its conformal class   In this paper, we study an extension of the CPE conjecture to manifolds $M$
which support a structure relating curvature to the geometry of a smooth map
$\varphi : M \to N$. The resulting system, denoted by $(\varphi-\mathrm{CPE})$,
is natural from the variational viewpoint and describes stationary points for
the integrated $\varphi$-scalar curvature functional restricted to metrics with
unit volume and constant $\varphi$-scalar curvature. We prove both a rigidity
statement for solutions to $(\varphi-\mathrm{CPE})$ in a conformal class, and a
gap theorem characterizing the round sphere among manifolds supporting
$(\varphi-\mathrm{CPE})$ with $\varphi$ a harmonic map.

35
The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci
12
The categories of this paper are: nucl-th
24
The categories of this paper are: dg-ga
4
The categories of this paper are: cond-mat
11
The categories of this paper are: hep-lat
36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
17
The categories of this paper are: q-fin
25
The categories of this paper are: patt-sol