Sub-Lorentzian Geometry on Anti-De Sitter Space

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dc.creatorChang, Der-Chen
dc.creatorMarkina, Irina
dc.creatorVasil'ev, Alexander
dc.date2007-08-07
dc.date2008-01-15
dc.date.accessioned2026-07-07T08:54:06Z
dc.date.available2026-07-07T08:54:06Z
dc.descriptionSub-Riemannian Geometry is proved to play an important role in many applications, e.g., Mathematical Physics and Control Theory. The simplest example of sub-Riemannian structure is provided by the 3-D Heisenberg group. Sub-Riemannian Geometry enjoys major differences from the Riemannian being a generalisation of the latter at the same time, e.g., geodesics are not unique and may be singular, the Hausdorff dimension is larger than the manifold topological dimension. There exists a large amount of literature developing sub-Riemannian Geometry. However, very few is known about its natural extension to pseudo-Riemannian analogues. It is natural to begin such a study with some low-dimensional manifolds. Based on ideas from sub-Riemannian geometry we develop sub-Lorentzian geometry over the classical 3-D anti-de Sitter space. Two different distributions of the tangent bundle of anti-de Sitter space yield two different geometries: sub-Lorentzian and sub-Riemannian. It is shown that the set of timelike and spacelike `horizontal' curves is non-empty and we study the problem of horizontal connectivity in anti-de Sitter space. We also use Lagrangian and Hamiltonian formalisms for both sub-Lorentzian and sub-Riemannian geometries to find geodesics.
dc.description31 pages, some technical errors are corrected
dc.identifierhttps://arxiv.org/abs/0708.0879
dc.identifierhttp://arxiv.org/abs/0708.0879
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/145814
dc.subjectDifferential Geometry
dc.subjectMathematical Physics
dc.subject53C50, 53C27, 83C65
dc.titleSub-Lorentzian Geometry on Anti-De Sitter Space
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