Harmonic points and the intersections of ovals
type: Item
instance of: scholarly article
title: Harmonic points and the intersections of ovals
zbMATH Open document ID: 0576.51008
DOI: 10.1007/BF00149366
author: Olga Fernandes
published in: Geometriae Dedicata
publication date: 1985-01-01T00:00:00Z
review text: Let X be a harmonic point with respect to an oval \({\mathcal O}\) of a finite projective plane of odd order [cf. \textit{T. G. Ostrom}, Geometry-von Staudt's point of view, Proc. Nato Adv. Study Inst., Bad Windsheim/Ger. 1980, 175-196 (1981; Zbl 0462.51003)]; let m be a line through X and f a non-identical (X,m)-elation. After proving a few preliminary results, the author shows that the maximal number of non-fixed points (under f) contained in the set \({\mathcal O}\cap f({\mathcal O})\) is 1 if m is tangent to \({\mathcal O}\) resp. 2 if m is secant to \({\mathcal O}\). For an (X,m)-transitive plane this result is then used for the study of the properties concerning the intersections of \({\mathcal O}\) with its images under the (X,m)-elations.
Mathematics Subject Classification ID: 51E20
Mathematics Subject Classification ID: 51E15
Mathematics Subject Classification ID: 05B25
zbMATH DE Number: 3921369
zbMATH Keywords: harmonic line
zbMATH Keywords: polar line of an exterior point
zbMATH Keywords: harmonic point with respect to an oval \({\mathcal O}\) of a finite
zbMATH Keywords: projective plane of odd order
zbMATH Keywords: (X,m)-elations
zbMATH Keywords: harmonic point with respect to an oval \({\mathcal O}\) of a finite projective plane of odd order
reviewed by: A. Bonisoli
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/bf00149366
OpenAlex ID: W2088851336
description: scientific article; zbMATH DE number 3921369