Hyper-reguli
type: Item
instance of: scholarly article
title: Hyper-reguli
zbMATH Open document ID: 0792.51001
DOI: 10.1007/BF01226806
published in: Journal of Geometry
publication date: 1994-01-31T00:00:00Z
review text: Let \(\pi\) be an affine Desarguesian plane of order \(q^ 4\), \(V\) the vector space of dimension \(2d\) whose elements are points of \(\pi\) and \(\Theta\) the projective space of dimension \(2d-1\) whose points are the 1- spaces in \(V\). Let \(N=(q^ d-1) (q-1)^{-1}\). A hyper-regulus is a set \(A=\{A_ 1,\dots,A_ N\}\) of mutually skew projective subspaces of \(\Theta\) of dimension \(d-1\) such that there exists another set \(B=\{B_ 1,\dots,B_ N\}\) of mutually skew projective subspaces of dimension \(d- 1\) with \(| A_ i \cap B_ j |=1\), \(i,j=1,\dots,N\). When \(d=2\), \(A\) and \(B\) are reguli in projective 3-space. Obvious examples come from André planes. A non-André example is constructed. Partial hyper- reguli are considered and some results concerning their extension to larger partial hyper-reguli and ultimately to hyper-reguli are obtained.
Mathematics Subject Classification ID: 51A40
Mathematics Subject Classification ID: 51E14
zbMATH DE Number: 493209
zbMATH Keywords: generalized André planes
zbMATH Keywords: hyper-reguli
author: Theodore G. Ostrom
reviewed by: William E. Cherowitzo
MaRDI profile type: Publication
cites work: Über nicht-Desarguessche Ebenen mit transitiver Translationsgruppe
cites work: Translation planes and derivation sets
cites work: Characterizations of regulus nets
cites work: A characterisation of spreads ovally-derived from Desarguesian spreads
cites work: Finite translation planes
cites work: Q5334781
full work available at URL: https://doi.org/10.1007/bf01226806
OpenAlex ID: W4256584542
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description: scientific article; zbMATH DE number 493209