Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A cornucopia of isospectral pairs of metrics on spheres with different
  local geometries   This article concludes the comprehensive study started in [Sz5], where the
first non-trivial isospectral pairs of metrics are constructed on balls and
spheres. These investigations incorporate 4 different cases since these balls
and spheres are considered both on 2-step nilpotent Lie groups and on their
solvable extensions. In [Sz5] the considerations are completely concluded in
the ball-case and in the nilpotent-case. The other cases were mostly outlined.
In this paper the isospectrality theorems are completely established on
spheres. Also the important details required about the solvable extensions are
concluded in this paper.
  A new so called anticommutator technique is developed for these
constructions. This tool is completely different from the other methods applied
in the field so far. It brought a wide range of new isospectrality examples.
Those constructed on geodesic spheres of certain harmonic manifolds are
particularly striking. One of these spheres is homogeneous (since it is the
geodesic sphere of a 2-point homogeneous space) while the other spheres,
although isospectral to the previous one, are not even locally homogeneous.
This shows how little information is encoded about the geometry (for instance,
about the isometries) in the spectrum of Laplacian acting on functions.

8
The categories of this paper are: hep-ex
23
The categories of this paper are: solv-int
36
The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th
0
The categories of this paper are: hep-ph
9
The categories of this paper are: nlin
25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas
22
The categories of this paper are: chao-dyn
17
The categories of this paper are: q-fin
20
The categories of this paper are: acc-phys
1
The categories of this paper are: cs
12
The categories of this paper are: nucl-th
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio