The inner and outer space of 2-dimensional Laguerre planes

B. Polster, G. F. Steinke

Research output: Contribution to journalArticleResearchpeer-review

6 Citations (Scopus)

Abstract

The classical 2-dimensional Laguerre plane is obtained as the geometry of non-trivial plane sections of a cylinder in ℝ3 with a circle in ℝ2 as base. Points and lines in ℝ3 define subsets of the circle set of this geometry via the affine non-vertical planes that contain them. Furthermore, vertical lines and planes define partitions of the circle set via the points and affine non-vertical lines, respectively, contained in them. We investigate abstract counterparts of such sets of circles and partitions in arbitrary 2-dimensional Laguerre planes. We also prove a number of related results for generalized quadrangles associated with 2-dimensional Laguerre planes.

Original languageEnglish
Pages (from-to)104-127
Number of pages24
JournalJournal of the Australian Mathematical Society
Volume62
Issue number1
Publication statusPublished - Feb 1997
Externally publishedYes

Keywords

  • Generalized quadrangle
  • Laguerre plane
  • Topological incidence geometry

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