Ricci-flat deformations of metrics with exceptional holonomy (Q2854228)

The main results are the following:NEWLINENEWLINENEWLINETheorem A. Let \(G=\text{SU}(n)\), \(\text{Sp}(n)\), \(\text{Spin}(7)\) or \(G_2\), and let \(M\) be a compact \(G\)-manifold. Then the moduli space \(W_G\) of \(G\)-metrics is open in the moduli space \(W_0\) of Ricci-flat metrics. Moreover, \(W_G\) is a smooth manifold and the natural map \(m:M_G\to W_G\), that sends a torsion-free \(G\)-structure to the metric it defines is a submersion.NEWLINENEWLINE Theorem B. Let \(G=\mathrm{Spin}(7)\) or \(G_2\) and \(M\) be an asymptotically cylindrical \(G\)-manifold. Then the moduli space \(W_G\) of \(G\)-metrics is open in the moduli space \(W_0\) of Ricci-flat metrics. Moreover, \(W_G\) is a smooth manifold and the natural map \(m:M_G\to W_G\) is a submersion.