Codazzi spinors and globally hyperbolic manifolds with special holonomy

Abstract

In this paper we describe the structure of Riemannian manifolds with a special kind of Codazzi spinors. We use them to construct globally hyperbolic Lorentzian manifolds with complete Cauchy surfaces, for any weakly irreducible holonomy representation with parallel spinors, t.m. with a holonomy group G ⋉ R n 2 ⊂ SO(1, n −1), where G ⊂ SO(n−2) is trivial or a product of groups SU(k), Sp(l), G2 or Spin(7).