Some differential-geometric properties of \(R\)-spaces
type: Item
instance of: scholarly article
title: Some differential-geometric properties of \(R\)-spaces
zbMATH Open document ID: 1022.53045
author: Hyunjung Song
published in: Tsukuba Journal of Mathematics
publication date: 2002-10-31T00:00:00Z
review text: An \(R\)-space is the orbit \(Ad(K)a\) of a point \(a\) belonging to the unit hypersphere \(S\) of \(T_0(G/K)\), where \(G/K\) is an irreducible Riemannian symmetric space and \(Ad(K)\) the adjoint representation group. \(R\)-spaces form a large class of homogeneous Riemannian manifolds. In the paper under review, new examples of homogeneous CR-submanifolds of a complex projective space are given, after investigating the relations between the complex structure and the restricted root system when \(G/K\) is Hermitian. Moreover, it is proved, through the expression of the covariant derivative of the second fundamental form of an \(R\)-sapce, that a cyclic-parallel \(R\)-space is necessarily parallel.
reviewed by: Giovanni Calvaruso
Mathematics Subject Classification ID: 53C35
zbMATH DE Number: 1822086
zbMATH Keywords: Riemannian symmetric spaces
zbMATH Keywords: homogeneous Riemannian manifolds
zbMATH Keywords: \(R\)-spaces
zbMATH Keywords: homogeneous CR-submanifolds
zbMATH Keywords: complex projective space
MaRDI profile type: Publication
Wikidata QID: Q115233486
full work available at URL: https://doi.org/10.21099/tkbjm/1496164288
OpenAlex ID: W1592179642
DOI: 10.21099/TKBJM/1496164288
description: scientific article; zbMATH DE number 1822086