Codazzi spinors and globally hyperbolic manifolds with special holonomy

Abstract

In this paper we examine the structure of Riemannian manifolds with a special kind of Codazzi tensors. We use them to construct globally hyperbolic Lorentzian manifolds with complete Cauchy hypersurfaces for any weakly irreducible holonomy representation with parallel spinors, i.e. with a holonomy group which is a semidirect product between ${\mathbb{R}}^{n-2}$ and one of $\1, SU(k), Sp(1), G_2$ and $Spin(7)$.

29 pages. to appear in: Mathematische Zeitschrift

References in corpus (1)

• The spaces of curvature tensors for holonomy algebras of Lorentzian manifolds