Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Invariant conformal metrics on S^n   In this paper we use the relationship between conformal metrics on the sphere
and horospherically convex hypersurfaces in the hyperbolic space for giving
sufficient conditions on a conformal metric to be radial under some constrain
on the eigenvalues of its Schouten tensor. Also, we study conformal metrics on
the sphere which are invariant by a $k-$parameter subgroup of conformal
diffeomorphisms of the sphere, giving a bound on its maximum dimension.
  Moreover, we classify conformal metrics on the sphere whose eigenvalues of
the Shouten tensor are all constant (we call them \emph{isoparametric conformal
metrics}), and we use a classification result for radial conformal metrics
which are solution of some $\sigma _k -$Yamabe type problem for obtaining
existence of rotational spheres and Delaunay-type hypersurfaces for some
classes of Weingarten hypersurfaces in $\h ^{n+1}$.

22
The categories of this paper are: chao-dyn
33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
21
The categories of this paper are: adap-org
36
The categories of this paper are: cmp-lg
1
The categories of this paper are: cs
28
The categories of this paper are: alg-geom
27
The categories of this paper are: comp-gas
25
The categories of this paper are: patt-sol
0
The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
7
The categories of this paper are: hep-th
13
The categories of this paper are: quant-ph
23
The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph