On the Alexandrov Topology of sub-Lorentzian Manifolds

Part of the Springer INdAM Series book series (SINDAMS, volume 5)


In the present work, we show that in contrast to sub-Riemannian geometry, in sub-Lorentzian geometry the manifold topology, the topology generated by an analogue of the Riemannian distance function and the Alexandrov topology based on causal relations, are not equivalent in general and may possess a variety of relations. We also show that ‘opened causal relations’ are more well-behaved in sub-Lorentzian settings.


Time Orientation Lorentzian Manifold Manifold Topology Horizontal Curve Lorentzian Geometry 
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© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of BergenNorway
  2. 2.Department of Mathematical SciencesDurham UniversityUK

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