Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Rigidity of Homogeneous Gradient Soliton Metrics and Related Equations   We prove structure results for homogeneous spaces that support a non-constant
solution to two general classes of equations involving the Hessian of a
function and an invariant 2-tensor. We also consider trace-free versions of
these systems. Our results generalize earlier rigidity results for gradient
Ricci solitons and warped product Einstein metrics. In particular, our results
apply to homogeneous gradient solitons of any invariant curvature flow and give
a new structure result for homogeneous conformally Einstein metrics.

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The categories of this paper are: nucl-ex
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The categories of this paper are: solv-int
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The categories of this paper are: chao-dyn
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The categories of this paper are: gr-qc
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The categories of this paper are: patt-sol
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The categories of this paper are: adap-org
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The categories of this paper are: math-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: econ
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The categories of this paper are: chem-ph
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The categories of this paper are: funct-an
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The categories of this paper are: astro-ph
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The categories of this paper are: q-bio
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The categories of this paper are: bayes-an
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The categories of this paper are: eess
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The categories of this paper are: atom-ph