Central collineations and the parallel axiom in stable planes

DOI10.1007/BF01447429zbMath0463.51016OpenAlexW1574963207MaRDI QIDQ1153554

Rainer Löwen

Publication date: 1981

Published in: Geometriae Dedicata (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01447429

zbMATH Keywords

reflectionsstable planesparallel axiomcentral collineationsreal and complex affine, projective and punctured projective planes

Mathematics Subject Classification ID

Topological linear incidence structures (51H10)

Related Items (18)

Actions of SO(3) on 4-dimensional stable planes ⋮ Stable planes ⋮ Ends of surface geometries, revisited ⋮ Ternary fields of compact projective planes ⋮ Stiffness in four-dimensional stable planes ⋮ Equivariant embeddings of low dimensional symmetric planes ⋮ Compact spreads and compact translation planes over locally compact fields ⋮ Blowing up points and embedding flat stable planes in the nonorientable compact surface of genus one ⋮ Linear geometries on the Moebius strip: A theorem of Skornyakov type ⋮ Quaternion Hermitian planes ⋮ Homogeneous translation groups ⋮ Generalized quadrangles constructed from topological Laguerre planes ⋮ Stabilizers of collineation groups of smooth stable planes ⋮ Duality in stable planes and related closure and kernel operations ⋮ Stable planes with isotropic points ⋮ A note on Hilbert and Beltrami systems ⋮ Multigroups and the foundations of geometry ⋮ A criterion for stability of planes

Cites Work

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• A Topological Characterization of the Dilation in E n
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