Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bel-Debever criteria for the classification of the Weyl tensors in
  higher dimensions   An extension to higher dimensions of the Bel-Debever characterization of the
Weyl tensor is considered. This provides algebraic conditions that uniquely
determine the multiplicity of a Weyl aligned null direction (WAND), and thus
the principal Weyl type, in a frame independent way. The specification of
several "subtypes" is also encompassed by the criteria. We further comment on a
Cartan-like geometrical interpretation of WANDs in terms of their invariance
properties under parallel transport around infinitesimal loops. As a result,
restrictions on the algebraic types permitted in spacetimes that admit a
recurrent/covariantly constant vector field are outlined.

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The categories of this paper are: q-fin
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The categories of this paper are: hep-lat
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The categories of this paper are: ao-sci
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The categories of this paper are: stat
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The categories of this paper are: math-ph
9
The categories of this paper are: nlin
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The categories of this paper are: atom-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: chem-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: patt-sol
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The categories of this paper are: cmp-lg
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The categories of this paper are: cs
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The categories of this paper are: q-alg
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The categories of this paper are: mtrl-th