Naturality of homogeneous metrics on stiefel manifolds \(SO(m + 1)/SO(m - 1)\)
type: Item
instance of: scholarly article
title: Naturality of homogeneous metrics on stiefel manifolds \(SO(m + 1)/SO(m - 1)\)
zbMATH Open document ID: 1190.53020
author: Mohamed Tahar Kadaoui Abbassi
author: Oldřich Kowalski
published in: Differential Geometry and its Applications
publication date: 2010-03-29T00:00:00Z
review text: The sphere tangent bundle \(T_1S^m\) of the standard sphere \(S^m\) with the natural action of the group \(SO(m+1))\) is a homogeneous manifold \(SO(m+1)/SO(m-1)\) and it is naturally identified with the Stiefel manifold \(V_2(\mathbb{R}^{m+1}) = SO(m+1)/SO(m-1) \) of 2-frames. The authors give a survey of results about different extensions of a Riemannian metric of a manifold \(M\) to the tangent bundle \(TM\) and the sphere tangent bundle \(T_1(M)\). They prove that so called \(g\)-natural metrics on \(T_1S^m\) correspond exactly to \(SO(m+1)\)-invariant metrics on the Stiefel manifold \(V_2(\mathbb{R}^{m+1})\).
reviewed by: Dmitri Alekseevsky
Mathematics Subject Classification ID: 53C07
Mathematics Subject Classification ID: 53C25
zbMATH DE Number: 5687508
zbMATH Keywords: sphere bundle
zbMATH Keywords: unit tangent bundle
zbMATH Keywords: Stiefel manifold
zbMATH Keywords: \(g\)-natural metric
MaRDI profile type: Publication
full work available at URL: j.difgeo.2009.05.007
OpenAlex ID: W2048474741
Wikidata QID: Q115357219
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DOI: 10.1016/J.DIFGEO.2009.05.007
description: scientific article; zbMATH DE number 5687508