Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Self-duality and associated parallel or cocalibrated ${\mathrm{G}}_2$
  structures   We find a remarkable family of $\mathrm{G}_2$ structures defined on certain
principal $\mathrm{SO}(3)$-bundles $P_\pm\longrightarrow M$ associated with any
given oriented Riemannian 4-manifold $M$. Such structures are always
cocalibrated. The study starts with a recast of the Singer-Thorpe equations of
4-dimensional geometry. These are applied to the Bryant-Salamon cons\-truction
of complete $\mathrm{G}_2$-holonomy metrics on the vector bundle of self- or
anti-self-dual 2-forms on $M$. We then discover new examples of that special
holonomy on disk bundles over ${\cal H}^4$ and ${\cal H}^2_{\mathbb{C}}$,
respectively, the real and complex hyperbolic space. Only in the end we present
the new $\mathrm{G}_2$ structures on principal bundles.

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The categories of this paper are: astro-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: chem-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
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The categories of this paper are: dg-ga
26
The categories of this paper are: bayes-an
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The categories of this paper are: nucl-ex
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The categories of this paper are: cond-mat
1
The categories of this paper are: cs
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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-th
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The categories of this paper are: math-ph
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The categories of this paper are: eess
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The categories of this paper are: supr-con