2008/08/13 by C. Denson Hill, C Denson Hill, Pawel Nurowski +3
Mathematics · Physics and Astronomy · #32V05 #53A55 #83C15 #Advanced Differential Geometry Research #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.CV #math.DG #msc:32V05 #msc:53A55 #msc:83C15
paper · pdf · doi:10.48550/arxiv.0808.1843
arxiv created 2008/08/13 · openalex publication_date 2008/08/13 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Starting from the classical notion of an oriented congruence (i.e. a foliation by oriented curves) in R3, we abstract the notion of an oriented congruence structure. This is a 3-dimensional CR manifold (M,H, J) with a preferred splitting of the tangent space TM=V⊕ H. We find all local invariants of such structures using Cartan's equivalence method refining Cartan's classification of 3-dimensional CR structures. We use these invariants and perform Fefferman like constructions, to obtain interesting Lorentzian metrics in four dimensions, which include explicit Ricci-flat and Einstein metrics, as well as not conformally Einstein Bach-flat metrics.