Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Einstein equations for a metric coupled to a trace-free symmetric tensor   There are described equations coupling a completely symmetric conformal
Killing or Codazzi tensor to the Einstein equations for a metric, in a manner
analogous to that used to obtain the Einstein-Maxwell equations by coupling a
two-form to the metric. Examples of solutions are constructed from mean
curvature zero immersions, affine spheres, isoparametric polynomials, and
regular graphs. There are deduced some constraints on the scalar curvature of
the metric occurring in a solution. Along the way, there are reviewed
Weitzenb\"ock formulas, vanishing theorems, and related results for conformal
Killing and divergence free Codazzi tensors.

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The categories of this paper are: atom-ph
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The categories of this paper are: supr-con
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The categories of this paper are: solv-int
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The categories of this paper are: patt-sol
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The categories of this paper are: chem-ph
7
The categories of this paper are: hep-th
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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: adap-org
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The categories of this paper are: econ
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-fin
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The categories of this paper are: astro-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: cs
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The categories of this paper are: chao-dyn