Abstract
Hilbert and Beltrami (line- ) systems were introduced by H. Mohrmann, Math. Ann. 85 (1922) p.177- 183. These systems give examples of non- desarguesian affine planes, in fact, the earliest known examples are of this type. We describe a construction for “generalized Beltrami systems”, and show that every such system defines a topological affine plane with point set ℝ2. Since our construction uses only the topological structure of ℝ2- planes, it is possible to iterate this process. As an application, we obtain an embeddability theorem for a class of two- dimensional stable planes, including Strambach’s exceptional SL2R- plane.
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Dedicated to Prof. Benno Artmann, on his 60th birthday.
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Stroppel, M. A note on Hilbert and Beltrami systems. Results. Math. 24, 342–347 (1993). https://doi.org/10.1007/BF03322342
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DOI: https://doi.org/10.1007/BF03322342