Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Parallel tractor extension and ambient metrics of holonomy split G_2   The holonomy of the ambient metrics of Nurowski's conformal structures
associated to generic real-analytic 2-plane fields on 5-manifolds is
investigated. It is shown that the holonomy is always contained in the split
real form G_2 of the exceptional Lie group, and is equal to G_2 for an open
dense set of 2-plane fields given by explicit conditions. In particular, this
gives an infinite-dimensional family of metrics of holonomy equal to split G_2.
These results generalize work of Leistner-Nurowski. The inclusion of the
holonomy in G_2 is established by proving an ambient extension theorem for
parallel tractors for conformal structures in general signature and dimension,
which is expected to be of independent interest. Parallel extension beyond the
critical order in even dimensions is considered in certain cases.

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The categories of this paper are: physics
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The categories of this paper are: mtrl-th
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The categories of this paper are: supr-con
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-lat
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-ex
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The categories of this paper are: nlin
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The categories of this paper are: gr-qc
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The categories of this paper are: math-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: plasm-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: quant-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: q-bio