Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Deformations of homogeneous associative submanifolds in nearly parallel
  $G_{2}$-manifolds   A nearly parallel $G_{2}$-manifold $Y$ is a Riemannian 7-manifold whose cone
$C(Y) = \mathbb{R}_{>0} \times Y$ has the holonomy group contained in ${\rm
Spin(7)}$. In other words, it is a spin 7-manifold with a real Killing spinor.
We have a special class of calibrated submanifolds called Cayley submanifolds
in $C(Y)$. An associative submanifold in $Y$ is a minimal 3-submanifold whose
cone is Cayley. We study its deformations, namely, Cayley cone deformations,
explicitly when it is homogeneous in the 7-sphere $S^{7}$.

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The categories of this paper are: atom-ph
30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex
12
The categories of this paper are: nucl-th
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol
24
The categories of this paper are: dg-ga
20
The categories of this paper are: acc-phys
37
The categories of this paper are: supr-con
21
The categories of this paper are: adap-org
7
The categories of this paper are: hep-th
0
The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an
11
The categories of this paper are: hep-lat
23
The categories of this paper are: solv-int
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The categories of this paper are: mtrl-th