Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Invariant Solutions of the Yamabe equation on the Koiso-Cao Soliton   We consider the non-trivial Ricci soliton on
$\mathbb{CP}^2\#\overline{\mathbb{CP}^2}$ constructed by Koiso and Cao. It is a
K\"ahler metric invariant by the $U(2)$ action on
$\mathbb{CP}^2\#\overline{\mathbb{CP}^2}$. We study its Yamabe equation and
prove it has exactly one $U(2)-$invariant solution up to homothecies.

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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-th
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The categories of this paper are: cond-mat
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The categories of this paper are: patt-sol
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The categories of this paper are: quant-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: ao-sci
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The categories of this paper are: math-ph
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The categories of this paper are: econ
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-ex
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The categories of this paper are: physics
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The categories of this paper are: eess
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The categories of this paper are: hep-ph
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The categories of this paper are: astro-ph