Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Laplacian Solitons and Symmetry in G_2-geometry   In this paper, it is shown that (with no additional assumptions) on a compact
7-dimensional manifold which admits a $G_2$-structure soliton solutions to the
Laplacian flow of R. Bryant can only be shrinking or steady. We also show that
the space of symmetries (vector fields that annihilate via the Lie derivative)
of a torsion-free $G_2$-structure on a compact 7-manifold is canonically
isomorphic to $H^1(M,\mathbb{R})$. Some comparisons with Ricci solitons are
also discussed, along with some future directions of exploration.

15
The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin
23
The categories of this paper are: solv-int
33
The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
7
The categories of this paper are: hep-th
21
The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph
20
The categories of this paper are: acc-phys
29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
22
The categories of this paper are: chao-dyn
13
The categories of this paper are: quant-ph
35
The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
16
The categories of this paper are: stat