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Nonholonomic Lorentzian Geometry on Some ℍ-Type Groups

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Abstract

We consider examples of ℍ-type Carnot groups whose noncommutative multiplication law gives rise to a smooth 2-step bracket generating distribution of the tangent bundle. In the contrast with the previous studies we furnish the horizontal distribution with the Lorentzian metric, which is nondegenerate metric of index 1, instead of a positive definite quadratic form. The causal character is defined. We study the reachable set by timelike future directed curves. The parametric equations of geodesics are obtained.

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Authors and Affiliations

  1. Department of Mathematics, University of Bergen, Johannes Brunsgate 12, Bergen, 5008, Norway

    Anna Korolko & Irina Markina

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  1. Anna Korolko
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  2. Irina Markina
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Correspondence to Anna Korolko.

Additional information

The authors are supported by a research grant of the Norwegian Research Council #177355/V30, by the European Science Foundation Research Networking Programme HCAA, and by the NordForsk Research Network.

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Korolko, A., Markina, I. Nonholonomic Lorentzian Geometry on Some ℍ-Type Groups. J Geom Anal 19, 864–889 (2009). https://doi.org/10.1007/s12220-009-9088-5

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  • DOI: https://doi.org/10.1007/s12220-009-9088-5

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