Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4606543 | Differential Geometry and its Applications | 2006 | 21 Pages |
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.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Thomas Leistner,