Geometric Control Theory and Sub-Riemannian Geometry pp 287-311

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

On the Alexandrov Topology of sub-Lorentzian Manifolds

Abstract

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.

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Copyright information

© 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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