Skip to main content
SpringerLink
Log in

The Beckman-Quarles theorem in Minkowski space for a spacelike square-distance

  • Published:
Archiv der Mathematik Aims and scope Submit manuscript

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

References

  1. A. D. Alexandrov, A Contribution to Chronogeometry. Canad. J. Math.19, 1119–1128 (1967).

    Google Scholar 

  2. A. D. Alexandrov andV. V. Ovchinnikova, Notes on the Foundations of Relativity Theory. Vestnik Leningrad. Univ.11, 95 (1953).

    Google Scholar 

  3. F. S. Beckman andD. A. Quarles, Jr., On Isometries of Euclidean Spaces. Proc. Amer. Math. Soc.4, 810–815 (1953).

    Google Scholar 

  4. W. Benz, Zur Charakterisierung der Lorentztransformationen. J. Geometry9, 29–37 (1977).

    Google Scholar 

  5. W.Benz, A Beckman-Quarles-Type-Theorem for Plane Lorentz Transformations. Math. Z. (to appear).

  6. W. Benz, Eine Beckmann-Quarles-Charakterisierung der Lorentztransformation des ℝn. Arch. Math.34, 550–559 (1981).

    Google Scholar 

  7. H.-J. Borchers andG. C. Hegerfeldt, The Structure of Space-time Transformations. Comm. Math. Phys.28, 259–266 (1972).

    Google Scholar 

  8. B.Farrahi, A Characterization of Isometries of Absolute Planes. Resultate Math. (to appear).

  9. A. V.Kuz'minyh, On a Characteristic Property of Isometric Mappings. Dokl. Akad. Nauk. SSSE, Tom226 (1976), Nr. 1.

  10. A. V. Kuz'minyh, A Minimal Condition that Determines a Lorentz Transformation. Sibirsk. Mat. Z.17, no. 6, 1321–1326, 1438 (1976).

    Google Scholar 

  11. J. A. Lester, Cone Preserving Mappings for Quadratic Cones over Arbitrary Fields. Canad. J. Math.29, 1247–1253 (1977).

    Google Scholar 

  12. J. A. Lester, Transformation ofn-Space Which Preserve a Fixed Square-Distance. Canad. J. Math.37, 392–395 (1979).

    Google Scholar 

  13. J. A. Lester, Some Properties of Non-Positive Definite Real Metric Vector Spaces. Utilitas Math.12, 327–333 (1977).

    Google Scholar 

  14. J. A. Lester andM. A. McKiernan. On Null-Cone Preserving Mappings. Math. Proc. Cambr. Phil. Soc.81, 455–462 (1977).

    Google Scholar 

  15. G.Martin, The Fundamental Theorem of Affine Geometry, (unpublished notes) 1976.

  16. E. M. Schröder, Zur Kennzeichnung der Lorentztransformationen. Aequations Math.19, 134–144 (1979).

    Google Scholar 

  17. E. C. Zeeman, Causality Implies the Lorentz Group. J. Math. Phys.5, 490–493 (1964).

    Google Scholar 

Download references

Author information

Author notes

  1. J. A. Lester

    Present address: Mathematisches Institut der Universität, Bundesstr. 55, D-2000, Hamburg 13

Authors and Affiliations

    Authors
    1. J. A. Lester
      View author publications

      You can also search for this author in PubMed Google Scholar

    Additional information

    This work was completed with the financial assistance of the Alexander von Humboldt Foundation.

    Rights and permissions

    Reprints and permissions

    About this article

    Cite this article

    Lester, J.A. The Beckman-Quarles theorem in Minkowski space for a spacelike square-distance. Arch. Math 37, 561–568 (1981). https://doi.org/10.1007/BF01234395

    Download citation

    • Received:

    • Issue Date:

    • DOI: https://doi.org/10.1007/BF01234395

    Keywords

    Search

    Navigation