Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Harmonic Forms on Manifolds with Non-Negative Bakry-\'Emery-Ricci
  Curvature   In this paper we prove that on a complete smooth metric measure space with
non-negative Bakry-\'Emery-Ricci curvature if the space of weighted L^2
harmonic one-forms is non-trivial then the weighted volume of the manifold is
finite and universal cover of the manifold splits isometrically as the product
of the real line with an hypersurface.

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The categories of this paper are: cs
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The categories of this paper are: cond-mat
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The categories of this paper are: nucl-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-th
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The categories of this paper are: eess
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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: funct-an
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The categories of this paper are: nucl-ex
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The categories of this paper are: supr-con
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The categories of this paper are: stat
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The categories of this paper are: q-bio
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The categories of this paper are: q-fin
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-ph