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|Title:||Conformal holonomy of C-spaces, Ricci-flat, and Lorentzian manifolds|
|Citation:||Differential Geometry and Its Applications, 2006; 24(5):458-478|
|Publisher:||Elsevier Science BV|
|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.|
|Appears in Collections:||Aurora harvest 6|
Pure Mathematics publications
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