Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Rigidity of noncompact complete manifolds with harmonic curvature   Let $(M,g)$ be a noncompact complete $n$-manifold with harmonic curvature and
positive Sobolev constant. Assume that $L_2$ norms of Weyl curvature and
traceless Ricci curvature are finite. We prove that $(M,g)$ is Einstein if $n
\ge 5$ and $L_{n/2}$ norms of Weyl curvature and traceless Ricci curvature are
small enough.

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The categories of this paper are: q-alg
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The categories of this paper are: funct-an
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The categories of this paper are: alg-geom
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The categories of this paper are: supr-con
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The categories of this paper are: q-fin
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The categories of this paper are: eess
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The categories of this paper are: nucl-th
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The categories of this paper are: physics
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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: nucl-ex
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The categories of this paper are: atom-ph
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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: chao-dyn