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Type: Journal article
Title: Conformal holonomy of C-spaces, Ricci-flat, and Lorentzian manifolds
Author: Leistner, T.
Citation: Differential Geometry and Its Applications, 2006; 24(5):458-478
Publisher: Elsevier Science BV
Issue Date: 2006
ISSN: 0926-2245
Abstract: The main result of this paper is that a Lorentzian manifold is locally conformally equivalent to a manifold with recurrent lightlike vector field and totally isotropic Ricci tensor if and only if its conformal tractor holonomy admits a 2-dimensional totally isotropic invariant subspace. Furthermore, for semi-Riemannian manifolds of arbitrary signature we prove that the conformal holonomy algebra of a C-space is a Berger algebra. For Ricci-flat spaces we show how the conformal holonomy can be obtained by the holonomy of the ambient metric and get results for Riemannian manifolds and plane waves. © 2006 Elsevier B.V. All rights reserved.
Keywords: holonomy groups
conformal holonomy
Lorentzian manifolds
plane waves
DOI: 10.1016/j.difgeo.2006.04.008
Appears in Collections:Aurora harvest 6
Pure Mathematics publications

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