Parallel spinors and parallel forms (Q1263816)

Let (M,g) be a complete simply connected irreducible Riemannian spin manifold. Then if (M,g) admits a non-zero parallel spinor then g is Ricci-flat. By employing the Berger-Simons theorem and some representation theory, the author deduces the dimension of the space of parallel spinors. This is achieved by giving a uniform description of the possible special structures in terms of parallel spinors and the bilinear invariants of the spin representations.