Desargues’ Theorem in Laguerre Planes
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Robert D. Knight
Abstract
Kahn [3] showed in 1980 that the Full Bundle Theorem characterizes ovoidal Laguerre planes. The spears and cycles (circles) of a general Laguerre plane can be represented by affine planes and points, respectively, of a near-linear space. In this space the Full Bundle Theorem takes a form analogous to the Veblen–Young Axiom for projective spaces. A proof that a form of Desargues’ Theorem within this near-linear space is equivalent to the Full Bundle Theorem is provided. Thus a Laguerre plane is desarguesian, in the sense of this paper, if, and only if, it is ovoidal.
Communicated by: R. Löwen
References
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Articles in the same Issue
- Frontmatter
- Polyhedral combinatorics of bisectors
- Explicit construction of decomposable Jacobians
- Some rigidity results on q-solitons
- Quasimorphisms on nonorientable surface diffeomorphism groups
- On nearly optimal paper Moebius bands
- Desargues’ Theorem in Laguerre Planes
- Simple obstructions and cone reduction
- The Bogomolov–Gieseker–Koseki inequality on surfaces with canonical singularities in arbitrary characteristic
- The simultaneous lattice packing-covering constant of octahedra
- An Abel–Jacobi theorem for metrized complexes of Riemann surfaces
- Exploring the interplay of semistable vector bundles and their restrictions on reducible curves
- Another proof of Segre’s theorem about ovals
Articles in the same Issue
- Frontmatter
- Polyhedral combinatorics of bisectors
- Explicit construction of decomposable Jacobians
- Some rigidity results on q-solitons
- Quasimorphisms on nonorientable surface diffeomorphism groups
- On nearly optimal paper Moebius bands
- Desargues’ Theorem in Laguerre Planes
- Simple obstructions and cone reduction
- The Bogomolov–Gieseker–Koseki inequality on surfaces with canonical singularities in arbitrary characteristic
- The simultaneous lattice packing-covering constant of octahedra
- An Abel–Jacobi theorem for metrized complexes of Riemann surfaces
- Exploring the interplay of semistable vector bundles and their restrictions on reducible curves
- Another proof of Segre’s theorem about ovals
