Journal
DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS
Volume 24, Issue 5, Pages 458-478Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.difgeo.2006.04.008
Keywords
holonomy groups; conformal holonomy; C-spaces; Lorentzian manifolds; plane waves
Categories
Ask authors/readers for more resources
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. (C) 2006 Elsevier B.V. All rights reserved.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available