Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Critical Point Equation And Contact Geometry   In this paper, we consider the CPE conjecture in the frame-work of
$K$-contact and $(\kappa, \mu)$-contact manifolds. First, we prove that if a
complete $K$-contact metric satisfies the CPE is Einstein and is isometric to a
unit sphere $S^{2n+1}$. Next, we prove that if a non-Sasakian $ (\kappa, \mu)
$-contact metric satisfies the CPE, then $ M^{3} $ is flat and for $ n > 1 $, $
M^{2n+1} $ is locally isometric to $ E^{n+1}\times S^{n}(4)$.

11
The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol
20
The categories of this paper are: acc-phys
4
The categories of this paper are: cond-mat
15
The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an
10
The categories of this paper are: q-bio
26
The categories of this paper are: bayes-an
5
The categories of this paper are: gr-qc
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
13
The categories of this paper are: quant-ph
24
The categories of this paper are: dg-ga