Flats and symmetry of homogeneous spaces
type: Item
instance of: scholarly article
title: Flats and symmetry of homogeneous spaces
zbMATH Open document ID: 0948.53029
author: Evangelia Samiou
published in: Mathematische Zeitschrift
publication date: 2000-01-01T00:00:00Z
review text: In a symmetric space of rank \(k\) every geodesic is contained in a flat, totally geodesic, connected, closed, \(k\)-dimensional submanifold, a so-called \(k\)-flat. Furthermore, the isometry group acts transitively on the set of pairs \((p,\Sigma)\), where \(\Sigma\) is a \(k\)-flat and \(p\in\Sigma\). A connected Riemannian manifold \(M\) with these properties is called \(k\)-flat homogeneous. We prove that \(k\)-flat homogeneity characterizes the symmetric spaces.
reviewed by: Evangelia Samiou
Mathematics Subject Classification ID: 53C35
Mathematics Subject Classification ID: 53C22
Mathematics Subject Classification ID: 53C30
zbMATH DE Number: 1462432
zbMATH Keywords: symmetric space
zbMATH Keywords: geodesic
zbMATH Keywords: \(k\)-flat homogeneity
MaRDI profile type: Publication
full work available at URL: s002090050507
OpenAlex ID: W2028634224
DOI: 10.1007/S002090050507
description: scientific article; zbMATH DE number 1462432