Circles in Riemannian symmetric spaces
type: Item
instance of: scholarly article
title: Circles in Riemannian symmetric spaces
zbMATH Open document ID: 0949.53037
author: Katsuya Mashimo
author: Koji Tojo
published in: Kodai Mathematical Journal
publication date: 2000-08-14T00:00:00Z
review text: Circles in Riemannian manifolds are defined by means of the canonical covariant derivative analogously to the standard circles in Euclidean spaces. The aim of this paper is to extend earlier results [see \textit{T. Adachi}, J. Math. Soc. Japan 48, 205-227 (1996; Zbl 0867.53048) and \textit{T. Adachi} and \textit{S. Maeda}, Tsukuba J. Math. 21, 29-42 (1997; Zbl 0891.53036)] to circles in compact Riemannian symmetric spaces. The main theorem says that every circle in such a space of rank one is the orbit of a one-parameter subgroup of isometries. Moreover, all homogeneous spaces with this property are either Riemannian globally symmetric spaces of rank one or Euclidean spaces.
reviewed by: Jan Slovák
Mathematics Subject Classification ID: 53C35
Mathematics Subject Classification ID: 53C40
zbMATH DE Number: 1333295
zbMATH Keywords: circle
zbMATH Keywords: symmetric space
Wikidata QID: Q115224546
MaRDI profile type: Publication
OpenAlex ID: W2074178491
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DOI: 10.2996/KMJ/1138043984
description: scientific article; zbMATH DE number 1333295