Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Pohozaev Identity on Warped Product Solitons   Warped product metrics are a class of Riemannian metrics on cross products $B
\times F$ which have been well studied and provide a rich set of examples. In
this paper we consider shrinking gradient Ricci solitons which are warped
product metrics. We prove that if the curvature of the metric is bounded and
the base $B$ has two dimensions, the metric must in fact be a cross product.
The theorem is a consequence of a Pohozaev-type identity. This closely
parallels results in the study of blow-ups of solutions to the reaction-
diffusion equation $\partial_t v = \Delta v + e^v$ in $\mathbb{R}^2$ .

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The categories of this paper are: nlin
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The categories of this paper are: q-alg
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The categories of this paper are: acc-phys
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The categories of this paper are: solv-int
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The categories of this paper are: funct-an
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The categories of this paper are: q-fin
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The categories of this paper are: bayes-an
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The categories of this paper are: math-ph
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The categories of this paper are: q-bio
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The categories of this paper are: nucl-ex
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The categories of this paper are: eess
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The categories of this paper are: astro-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-th
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The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-th