Parallelisms of \(\text{PG}(3, {\mathbb R})\) composed of non-regular spreads

DOI10.1007/s00010-011-0081-2zbMath1222.51009OpenAlexW2069082369MaRDI QIDQ543292

Dieter Betten, Rolf Riesinger

Publication date: 17 June 2011

Published in: Aequationes Mathematicae (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00010-011-0081-2

zbMATH Keywords

flockparallelismClifford parallelismKlein quadrictopological parallelismThas-Walker constructionpiecewise regular spreadprojective 3-spacerotational spread

Mathematics Subject Classification ID

Translation planes and spreads in linear incidence geometry (51A40) Linear incidence geometric structures with parallelism (51A15) Line geometries and their generalizations (51M30) Topological linear incidence structures (51H10)

Related Items (6)

A characterization of Clifford parallelism by automorphisms ⋮ Compactness of the automorphism group of a topological parallelism on real projective 3-space ⋮ Clifford parallelism: old and new definitions, and their use ⋮ Rotational spreads and rotational parallelisms and oriented parallelisms of \(\mathrm{PG}(3,\mathbb{R})\) ⋮ Parallelisms of \(\mathrm{PG}(3,\mathbb{R})\) admitting a 3-dimensional group ⋮ Automorphisms of some topological regular parallelisms of \(\mathrm{PG}(3, \mathbb{R})\)

Cites Work

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• Coset switching in parallelisms
• Generalized line stars and topological parallelisms of the real projective 3-space
• Examples of rigid, topological spreads of the real projective 3- space.
• Parallelism-inducing groups
• Piecewise regular spreads
• Spreads admitting net generating regulizations
• Minimal parallelism-inducing groups
• Nicht-desarguessche 4-dimensionale Ebenen
• Topological parallelisms of the real projective 3-space
• Constructing topological parallelisms of PG(3, ℝ) via rotation of generalized line pencils
• Computational line geometry
• Hyperflock determining line sets and totally regular parallelisms of \(\text{PG}(3,\mathbb{R})\)

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