Skip to main content
SpringerLink
Log in

Polarities in finite 2-uniform projective Hjelmslev planes

  • Published:
Geometriae Dedicata Aims and scope Submit manuscript

Abstract

In this paper we deal with polarities in finite projective Hjelmslev planes. A polarity is an involutory one-to-one mapping π of the points onto the lines and of the lines onto the points such that the incidence relation and the neighbor relation are preserved. Most of the results are obtained in the case of 2-uniform PH-planes. In a forthcoming paper [5], we shall deal with the case of n-uniform (n > 2) PH-planes.

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. Cronheim, A., ‘Dual Numbers, Witt Vectors and Hjelmslev Planes’, Geom. Dedicata, 7 (1978), 287–302.

    Google Scholar 

  2. Dembowski, P., Finite Geometries, Springer, Berlin, Heidelberg, New York, 1968.

    Google Scholar 

  3. Hirschfeld, J. W. P., Projective Geometries over Finite Fields, Clarendon Press, Oxford, 1979.

    Google Scholar 

  4. Hughes, D. R. and Piper, F. C., Projective Planes, Springer Verlag, 1973.

  5. Keppens, D., ‘Polarities in n-Uniform Projective Hjelmslev Planes’ (manuscript).

  6. Keppens, D., ‘Polarities in Projective Hjelmslev Spaces and Related Geometries’ (in preparation).

  7. Kleinfeld, E., ‘Finite Hjelmslev Planes’, Illinois J. Math. 3 (1959), 403–407.

    Google Scholar 

  8. Klingenberg, W., ‘Desarguessche Ebenen mit Nachbarelementen’, Abh. Math. Sem. Univ. Hamb. 20 (1955), 97–111.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Seminar of Geometry and Combinatorics, State University of Gent, Krijgslaan 281, B-9000, Gent, Belgium

    Dirk Keppens

Authors
  1. Dirk Keppens
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

The author's research was supported by I.W.O.N.L. grant No. 840037.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Keppens, D. Polarities in finite 2-uniform projective Hjelmslev planes. Geom Dedicata 24, 51–76 (1987). https://doi.org/10.1007/BF00159747

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00159747

Keywords

Search

Navigation