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arXiv · hep-th/0612171

The Ricci Curvature of Half-flat Manifolds

Tibra Ali·Gerald B. Cleaver
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Abstract

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 Kähler moduli space of type II string theories on these half-flat manifolds.

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Tibra Ali, Gerald B. Cleaver. 2007-05-01. The Ricci Curvature of Half-flat Manifolds. https://doi.org/10.1088/1126-6708%2F2007%2F05%2F009

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