Codazzi spinors and globally hyperbolic manifolds with special holonomy

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 g...

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Bibliographic Details
Published in:arXiv.org 2007-04
Main Authors: Baum, Helga, Müller, Olaf
Format: Article
Language:English
Subjects:
Hyperspaces
Manifolds (mathematics)
Riemann manifold
Tensors
Online Access:Get full text
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Summary: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 \(Spin(7)\).
ISSN:2331-8422