Codazzi spinors and globally hyperbolic manifolds with special holonomy

Details Codazzi spinors and globally hyperbolic manifolds with special holonomy Codazzi spinors and globally hyperbolic manifolds with special holonomy

2007-04-27

arxiv.org/abs/0704.3725v1

Mathematics

Differential Geometry

29 pages. to appear in: Mathematische Zeitschrift

Scientific paper

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 $\R^{n-2}$ and one of $\1, SU(k), Sp(1), G_2$ and $Spin(7)$.

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