Basic transformations of symmetric R-spaces
type: Item
instance of: scholarly article
title: Basic transformations of symmetric R-spaces
zbMATH Open document ID: 0705.53024
author: Masaru Takeuchi
published in: Osaka Journal of Mathematics
publication date: 1988-01-01T00:00:00Z
review text: The irreducible symmetric R-spaces form an important class of compact symmetric spaces. Each of them admits a geometrically natural ``group of basic transformations'', which is greater than the corresponding group of isometries. (This is, e.g., the group of conformal transformations for a sphere, and the group of projective transformations for every classical projective space \(P_ n(F))\). The author gives a characterization of these basic groups in terms of Riemannian geometry. For each compact rank one symmetric space (except the sphere), the basic group is the group of all diffeomorphisms which preserve the system of all so-called Helgason spheres. For any irreducible symmetric R-space of rank greater than one, the basic group is the group of all diffeomorphisms which preserve the arithmetic distance d. (Let us note that the arithmetic distance is a metrical invariant derived from the system of Helgason spheres).
Mathematics Subject Classification ID: 53C35
zbMATH DE Number: 4157420
zbMATH Keywords: symmetric R-spaces
zbMATH Keywords: group of basic transformations
zbMATH Keywords: Helgason spheres
zbMATH Keywords: arithmetic distance
reviewed by: Oldřich Kowalski
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4157420