Ricci-flat deformations and special holonomy

2010/08/03 by Nordström, Johannes
#53C25 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1008.0663

Abstract

Let G be one of the Ricci-flat holonomy groups SU(n), Sp(n), Spin(7) or G₂, and M a compact manifold of dimension 2n, 4n, 8 or 7, respectively. We prove that the natural map from the moduli space of torsion-free G-structures on M to the moduli space of Ricci-flat metrics is open, and that the image is a smooth manifold. For the exceptional cases G = Spin(7) and G₂ we extend the result to asymptotically cylindrical manifolds.

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