Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nearly Kaehler and nearly parallel G_2-structures on spheres   In some other context, the question was raised how many nearly K\"ahler
structures exist on the sphere $\S^6$ equipped with the standard Riemannian
metric. In this short note, we prove that, up to isometry, there exists only
one.
  This is a consequence of the description of the eigenspace to the eigenvalue
$\lambda = 12$ of the Laplacian acting on 2-forms. A similar result concerning
nearly parallel $\G_2$-structures on the round sphere $\S^7$ holds, too. An
alternative proof by Riemannian Killing spinors is also indicated.

24
The categories of this paper are: dg-ga
17
The categories of this paper are: q-fin
9
The categories of this paper are: nlin
6
The categories of this paper are: astro-ph
34
The categories of this paper are: chem-ph
15
The categories of this paper are: nucl-ex
28
The categories of this paper are: alg-geom
7
The categories of this paper are: hep-th
11
The categories of this paper are: hep-lat
18
The categories of this paper are: econ
5
The categories of this paper are: gr-qc
10
The categories of this paper are: q-bio
25
The categories of this paper are: patt-sol
23
The categories of this paper are: solv-int
26
The categories of this paper are: bayes-an
4
The categories of this paper are: cond-mat