Invariants and Infinitesimal Transformations for Contact Sub-Lorentzian Structures on 3-Dimensional Manifolds

2013/12/31 by Marek Grochowski, Ben Warhurst · 2 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Conformal map #Geometric Analysis and Curvature Flows #Geometry #Homogeneous space #Homotopy and Cohomology in Algebraic Topology #Infinitesimal #Invariant (physics) #Killing vector field #Lie group #Manifold (fluid mechanics) #Mathematical analysis #Mathematical physics #Mathematics #Physics #Pure mathematics #Symmetry (geometry) #math.DG #msc:53B30 #msc:53C30

paper · pdf · doi:10.3842/sigma.2015.031

published in Symmetry Integrability and Geometry Methods and Applications (National Academy of Sciences of Ukraine)

arxiv created 2015/04/17 · openalex publication_date 2015/04/17 · arxiv updated 2015/04/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

In this article we develop some elementary aspects of a theory of symmetry in sub-Lorentzian geometry. First of all we construct invariants characterizing isometric classes of sub-Lorentzian contact 3 manifolds. Next we characterize vector fields which generate isometric and conformal symmetries in general sub-Lorentzian manifolds. We then focus attention back to the case where the underlying manifold is a contact 3 manifold and more specifically when the manifold is also a Lie group and the structure is left-invariant.

Citations

• Nonholonomic Lorentzian geometry on some \mathbb H-type groups
• Differential equations and para-CR structures
• Shortest paths for sub-Riemannian metrics on rank-two distributions
• Conformal equivalence of sub-Riemannian 3D contact structures on Lie groups
• 3-dimensional left-invariant sub-Lorentzian contact structures
• Geodesics on H-type quaternion groups with sub-Lorentzian metric and their physical interpretation