Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Ricci Curvature of Half-flat Manifolds   We derive expressions for the Ricci curvature tensor and scalar in terms of
intrinsic torsion classes of half-flat manifolds by exploiting the relationship
between half-flat manifolds and non-compact $G_2$ holonomy manifolds. Our
expressions are tested for Iwasawa and more general nilpotent manifolds. We
also derive expressions, in the language of Calabi-Yau moduli spaces, for the
torsion classes and the Ricci curvature of the \emph{particular} half-flat
manifolds that arise naturally via mirror symmetry in flux compactifications.
Using these expressions we then derive a constraint on the K\"ahler moduli
space of type II string theories on these half-flat manifolds.

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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: ao-sci
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The categories of this paper are: gr-qc
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The categories of this paper are: acc-phys
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The categories of this paper are: astro-ph
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The categories of this paper are: funct-an
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The categories of this paper are: hep-ph
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The categories of this paper are: supr-con
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The categories of this paper are: chem-ph
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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: econ
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The categories of this paper are: cond-mat
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The categories of this paper are: stat
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The categories of this paper are: plasm-ph