Clifford parallelism: old and new definitions, and their use

DOI10.1007/s00022-012-0118-2zbMath1258.51001OpenAlexW1989553738MaRDI QIDQ1928604

Dieter Betten, Rolf Riesinger

Publication date: 3 January 2013

Published in: Journal of Geometry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00022-012-0118-2

zbMATH Keywords

complexificationtopological parallelismelliptic displacementfocal line of a regular spreadimaginary quadricsKlein's correspondence of line geometry

Mathematics Subject Classification ID

Linear incidence geometric structures with parallelism (51A15) Line geometries and their generalizations (51M30) Topological linear incidence structures (51H10)

Related Items (9)

A characterization of Clifford parallelism by automorphisms ⋮ Automorphisms of a Clifford-like parallelism ⋮ Clifford-like parallelisms ⋮ Rotational spreads and rotational parallelisms and oriented parallelisms of \(\mathrm{PG}(3,\mathbb{R})\) ⋮ Clifford parallelisms and external planes to the Klein quadric ⋮ Pencilled regular parallelisms ⋮ Characterising Clifford parallelisms among Clifford-like parallelisms ⋮ Clifford parallelisms defined by octonions ⋮ Variations on a theme: Clifford's parallelism in elliptic space

Cites Work

• Generalized Clifford parallelisms
• Parallelisms of \(\text{PG}(3, {\mathbb R})\) composed of non-regular spreads
• Regular parallelisms in kinematic spaces
• Generalized line stars and topological parallelisms of the real projective 3-space
• Examples of rigid, topological spreads of the real projective 3- space.
• Projektive Doppelräume
• Eine inzidenzgeometrische Kennzeichnung projektiver kinematischer Räume
• Bestimmung aller projektiven Doppelräume
• Parallelisms of projective spaces
• Nicht-desarguessche 4-dimensionale Ebenen
• Topological parallelisms of the real projective 3-space
• Clifford parallels in elliptic (2𝑛-1)-spaces and isoclinic 𝑛-planes in euclidean 2𝑛-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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