Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Flows of G_2 Structures, I   This is a foundational paper on flows of G_2 Structures. We use local
coordinates to describe the four torsion forms of a G_2 Structure and derive
the evolution equations for a general flow of a G_2 Structure on a 7-manifold.
Specifically, we compute the evolution of the metric, the dual 4-form, and the
four independent torsion forms. In the process we obtain a simple new proof of
a theorem of Fernandez-Gray.
  As an application of our evolution equations, we derive an analogue of the
second Bianchi identity in G_2-geometry which appears to be new, at least in
this form. We use this result to derive explicit formulas for the Ricci tensor
and part of the Riemann curvature tensor in terms of the torsion. These in turn
lead to new proofs of several known results in G_2 geometry.

13
The categories of this paper are: quant-ph
12
The categories of this paper are: nucl-th
34
The categories of this paper are: chem-ph
1
The categories of this paper are: cs
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The categories of this paper are: nucl-ex
14
The categories of this paper are: math-ph
21
The categories of this paper are: adap-org
19
The categories of this paper are: eess
3
The categories of this paper are: physics
28
The categories of this paper are: alg-geom
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The categories of this paper are: q-fin
18
The categories of this paper are: econ
32
The categories of this paper are: atom-ph
11
The categories of this paper are: hep-lat
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The categories of this paper are: nlin
7
The categories of this paper are: hep-th