Maximal convex metrics on some classical metric spaces
type: Item
instance of: scholarly article
title: Maximal convex metrics on some classical metric spaces
zbMATH Open document ID: 0679.54028
DOI: 10.1007/BF00182113
published in: Geometriae Dedicata
publication date: 1989-01-01T00:00:00Z
review text: A metric d is said to have maximal symmetry iff its isometry group is not properly contained in the isometry group of any metric equivalent to d. Theorem. Every convex, two-point homogeneous metric for which small spheres are connected has maximal symmetry. Corollary. The standard metrix on \({\mathbb{E}}^ n\), \({\mathbb{S}}^ n\), \({\mathbb{R}}{\mathbb{P}}^ n\), \({\mathbb{C}}{\mathbb{P}}^ n\), \({\mathbb{Q}}{\mathbb{P}}^ n\), \({\mathbb{H}}^ n\), \({\mathbb{C}}{\mathbb{H}}^ n\), \({\mathbb{Q}}{\mathbb{H}}^ n\), Cay \({\mathbb{P}}^ 2\), Cay \({\mathbb{H}}^ 2\) have maximal symmetry.
Mathematics Subject Classification ID: 54E35
Mathematics Subject Classification ID: 54F65
Mathematics Subject Classification ID: 57N15
Mathematics Subject Classification ID: 54H15
Mathematics Subject Classification ID: 54E40
zbMATH DE Number: 4113522
zbMATH Keywords: isometry group
zbMATH Keywords: convex, two-point homogeneous metric
zbMATH Keywords: maximal symmetry
author: Philip L. Bowers
reviewed by: Hansjoachim Groh
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4113522