Conformal holonomy of C-spaces, Ricci-flat, and Lorentzian manifolds

By Thomas Leistner. 2005

69 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Astronomy and Astrophysics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/6c382fd5857d9b1e086f10c2796c61e352a9bcb2

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Dmitri Alekseevsky
2. Anton S. Galaev
3. Vicente Cortés
4. Thomas Leistner

In Astronomy and Astrophysics

1. Dmitri Alekseevsky
2. Anton S. Galaev
3. Vicente Cortés
4. Thomas Leistner

In Geometry and Topology

1. Dmitri Alekseevsky
2. Anton S. Galaev
3. Vicente Cortés
4. Thomas Leistner

Citations in the corpus

• Cones over pseudo-Riemannian manifolds and their holonomy (2007, methodology): “Applying Theorem 4.2 in [ 16 ] to the Lorentzian situation it follows that”
• Maximally homogeneous para-CR manifolds of semisimple type (2006, unknown): “These results were obtained in [71] and [72].”