Holonomy rigidity for Ricci-flat metrics (Q2633067)

The main result of the present paper is the following theorem (Rigidity of the holonomy group): Let \((M,g)\) be a compact Riemannian manifold whose universal covering is spin and carries a parallel spinor. If \(g_t, t\in I :=[0,T]\) is a smooth family of Ricci-flat metrics such that \(g_0=g\), then \(\text{Hol}(M,g_t)\) is conjugate to \(\text{Hol}(M,g)\) in \(\mathrm{GL}(n,R)\), where \(\text{Hol}(M,g)\) is the holonomy group of \((M,g)\).