Skip to main content
SpringerLink
Log in

Normal Forms of Germs of Contact Sub-Lorentzian Structures on R3. Differentiability of the Sub-Lorentzian Distance Function

  • Published:
Journal of Dynamical and Control Systems Aims and scope Submit manuscript

Abstract

The aim of this paper is to construct certain normal forms for germs of contract sub-Lorentzian metrics in R3. Using them we show that there are regions in which longest curves are necessarily timelike, and where the local sub-Lorentzian distance function is smooth. By the way, we compute the null conjugate locus of a point.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. A. A. Agrachev, El-H. Chakir El-A., and J. P. Gauthier, Sub-Riemannian metrics on ℝ3. Proc. Conf. Canad. Math. Soc. 25 (1998).

  2. El.-H. Alaoui, J.-P. Gauthier, and I. Kupka, Small sub-Riemannian balls in ℝ3. J. Dynam. Control Systems 2 (1996), No. 3, 359-421.

    Google Scholar 

  3. J. K. Beem, P. E. Ehrlich, and K. L. Easley, Global Lorentzian geometry. Marcel Dekker (1996).

  4. M. Golubitsky and V. Guillemin, Stable mappings and their singularities. Spinger-Verlag, New York (1973).

    Google Scholar 

  5. M. Grochowski, Differential properties of the sub-Riemannian distance function. Bull. Polish Acad. Sci. 50 (2002), No. 1.

    Google Scholar 

  6. M. Grochowski, Geodesics in the sub-Lorentzian geometry. Bull. Polish Acad. Sci. 50 (2002), No. 2.

    Google Scholar 

  7. M. Grochowski, On the Heisenberg sub-Lorentzian metric on ℝ3. Preprint Singularity Theory Seminar, S. Janeczko (ed.), Faculty of Mathemathics and Information Sciences, Warsaw University of Technology (2002).

Download references

Author information

Authors and Affiliations

  1. Faculty of Mathematics, Cardinal Stefan Wyszyński University in Warsaw, ul. Dewajtis 5, 01-815, Warszawa, Poland

    Marek Grochowski

Authors
  1. Marek Grochowski
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Grochowski, M. Normal Forms of Germs of Contact Sub-Lorentzian Structures on R3. Differentiability of the Sub-Lorentzian Distance Function. Journal of Dynamical and Control Systems 9, 531–547 (2003). https://doi.org/10.1023/A:1025696302287

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1025696302287

Search

Navigation