Faserungen, die aus Reguli mit einem gemeinsamen Geradenpaar zusammengesetzt sind. (About spreads which are built up by reguli with two lines in common)
type: Item
instance of: scholarly article
title: Faserungen, die aus Reguli mit einem gemeinsamen Geradenpaar zusammengesetzt sind. (About spreads which are built up by reguli with two lines in common)
zbMATH Open document ID: 0787.51005
DOI: 10.1007/BF01225773
published in: Journal of Geometry
publication date: 1993-01-17T00:00:00Z
review text: Using Plücker coordinates, the author explicitly describes slight deformations of an ordinary spread in \(P_ 3\mathbb{R}\) leading to 4- dimensional topological translation planes with 6-dimensional automorphism group [cf. \textit{D. Betten}, Math. Z. 128, 129-151 (1972; Zbl 0231.50011)]. For a fixed, sufficiently small \(\varepsilon > 0\), one of the Plücker coordinates has the form \(uv(1-\varepsilon \sin t\cdot \cos t)\cos t\), the others are given by similar expressions.
Mathematics Subject Classification ID: 51A40
Mathematics Subject Classification ID: 51H10
Mathematics Subject Classification ID: 51M30
zbMATH DE Number: 98736
zbMATH Keywords: spreads
zbMATH Keywords: \(H\)-dimensional translation planes
author: Rolf Riesinger
reviewed by: Helmut Salzmann
MaRDI profile type: Publication
cites work: Über nicht-Desarguessche Ebenen mit transitiver Translationsgruppe
cites work: 4-dimensionale Translationsebenen mit 8-dimensionaler Kollineationsgruppe
cites work: 4-dimensionale Translationsebenen mit irreduzibler Kollineationsgruppe
cites work: 4-dimensionale Translationsebenen mit genau einer Fixrichtung
cites work: 4-dimensionale Translationsebenen mit 7-dimensionaler Kollineationsgruppe.
cites work: The construction of translation planes from projective spaces
cites work: Q5801353
cites work: Q5679059
cites work: Q3694152
cites work: Q5820985
cites work: Examples of rigid, topological spreads of the real projective 3- space.
full work available at URL: https://doi.org/10.1007/bf01225773
OpenAlex ID: W2025160110
description: scientific article; zbMATH DE number 98736