Skip to main content
SpringerLink
Log in

A new class of planar π-spaces and some related topics: (n,d)-systems and (σ,n)-spaces

  • Published:
Journal of Geometry Aims and scope Submit manuscript

Summary

Planar spaces with planes isomorphic to PG(d, Q) or to AG(d, Q), with d ⩾3, are presented, and a natural generalization of π-spaces, namely the (σ, n)-spaces, is also studied. For this purpose, we use the language of (n, d)-systems, which was introduced and studied by G. Tallini [13], and for which we give a brief sketch of the theory.

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

Bibliography

  1. E. Bertini, Introduzione alla geometria proiettiva degli iperspazi, Pisa, E. Spoerri, 1907.

    Google Scholar 

  2. A. E. Brower, On the non existence of certain planar spaces, Mathematisch Centrum Amsterdam, 1978.

    Google Scholar 

  3. F. Buekenhout et R. Deherder, Espaces linéaires finis à plans isomorphes, Bull. Soc. Math. Belg. 23(1971) 348–359.

    Google Scholar 

  4. P.V. Ceccherini, Sulla nozione di spazio grafico, Rend. Mat. e Appl. (5) 26 (1967) 78–98.

    Google Scholar 

  5. P.V. Ceccherini, Collineazioni e semicollineazioni tra spazi affini o proiettivi, Rend. Mat. e Appl. (5) 26 (1907) 309–348.

    Google Scholar 

  6. P.V. Ceccherini, A. Dragomir, Combinazioni generalizzate, q-coefficienti binomiali e spazi grafici, Atti Convegno di Geometria Combinatoria e sue Applicazioni (Perugia, 1970), 137–158. Oderisi, Gubbio, 1971.

    Google Scholar 

  7. A. Delandtsheer, Finite planar spaces with isomorphic planes, Discrete Math. 42 (1982) 161–176.

    Google Scholar 

  8. J.W.P. Hirschfeld, Projective geometry over finite fields. Oxford University Press, 1979.

  9. D.A. Leonard, Finite π-spaces, Geometriae Dedicata 12 (1982) 215–218.

    Google Scholar 

  10. G. Peano, Calcolo geometrico secondo l'Ausdehnungslehre di H. Grassmann, preceduto dalle operazioni della logica deduttiva. Torino, Bocca, 1888 (Chapter IX).

    Google Scholar 

  11. B. Segre, Lectures on modern geometry. With an Appendix by L. Lombardo Radice. Roma, Cremonese, 1961.

    Google Scholar 

  12. B. Segre, Teoria di Galois, fibrazioni proiettive e geometrie non desarguesiane, Ann. di Mat. (4) 64 (1964) 1–76.

    Google Scholar 

  13. G. Tallini, Lezioni di Geometria III. Appunti raccolti da A. Ippolito (a.a. 1984–85), Cap. IV. Istituto Matematico “G. Castelnuovo”, Università di Roma “La Sapienza”, 1985.

Download references

Author information

Authors and Affiliations

  1. Dipartimento di Matematica “G. Castelnuovo”, Università di Roma “La Sapienza”, Città Universitaria, 00185, Roma, Italy

    P. V. Ceccherini & G. Tallini

Authors
  1. P. V. Ceccherini
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. G. Tallini
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Dedicated to Professor M. Barner on the occasion of his 65th birthday

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ceccherini, P.V., Tallini, G. A new class of planar π-spaces and some related topics: (n,d)-systems and (σ,n)-spaces. J Geom 27, 69–86 (1986). https://doi.org/10.1007/BF01230335

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01230335

Keywords

Search

Navigation