2005/07/04 by Thomas Leistner · 1 citation
Mathematics · Medicine · Physics and Astronomy · #Advanced Differential Geometry Research #Curvature #Field (mathematics) #Geometric Analysis and Curvature Flows #Geometry #Holonomy #Manifold (fluid mechanics) #Mathematical analysis #Mathematical physics #Mathematics #Ophthalmology and Eye Disorders #Parallel transport #Pure mathematics #Ricci-flat manifold #Riemann curvature tensor #Scalar curvature #Vector field #math.DG #msc:53B30 #msc:53C29 #msc:53C50
paper · pdf · doi:10.1016/j.geomphys.2005.11.010
published as J. Geom. Phys. 56 (2006), no. 10, 2117-2134 · 18 pages
arxiv created 2005/07/04 · openalex publication_date 2005/12/28 · arxiv updated 2012/08/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
A pp-wave is a Lorentzian manifold with a parallel light-like vector field satisfying a certain curvature condition. We introduce generalisations of pp-waves, on one hand by allowing the vector field to be recurrent and on the other hand by weakening the curvature condition. These generalisations are related to the screen holonomy of the Lorentzian manifold. While pp-waves have a trivial screen holonomy there are no restrictions on the screen holonomy of the manifolds with the weaker curvature condition.