Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Einstein tori and crooked surfaces   In hyperbolic space, the angle of intersection and distance classify pairs of
totally geodesic hyperplanes. A similar algebraic invariant classifies pairs of
hyperplanes in the Einstein universe. In dimension 3, symplectic splittings of
a 4-dimensional real symplectic vector space model Einstein hyperplanes and the
invariant is a determinant. The classification contributes to a complete
disjointness criterion for crooked surfaces in the 3-dimensional Einstein
universe.

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The categories of this paper are: astro-ph
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The categories of this paper are: adap-org
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The categories of this paper are: hep-th
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The categories of this paper are: q-bio
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The categories of this paper are: econ
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-ex
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The categories of this paper are: dg-ga
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: acc-phys
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The categories of this paper are: nlin
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The categories of this paper are: eess
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The categories of this paper are: atom-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: chem-ph