Dimension des orbites d'une action de \({\mathbb{R}}^ p\) sur une variété compacte. (The dimension of orbits of \({\mathbb{R}}^ p\)-actions on compact manifolds)
type: Item
instance of: scholarly article
title: Dimension des orbites d'une action de \({\mathbb{R}}^ p\) sur une variété compacte. (The dimension of orbits of \({\mathbb{R}}^ p\)-actions on compact manifolds)
zbMATH Open document ID: 0671.57026
DOI: 10.1007/BF02566765
published in: Commentarii Mathematici Helvetici
publication date: 1988-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/140120
review text: Let M be a compact, connected m-manifold without boundary. The rank of M is the largest number of commuting, everywhere linearly independent vector fields on M and is denoted rk(M). If \(\phi\) : \(R^ p\times M\to M\) is a smooth action, the authors define m(\(\phi)\) to be the minimum orbit dimension and relate this number to the rank rk(M). Precisely, they prove the following: Theorem. Let \(M\neq T^ m\) be a compact, connected m-manifold, \(\partial M=\emptyset\), and let \(rk(M)=k\). Then every \(C^{\infty}\) action \(R^ p\times M\to M\) has some orbit of dimension strictly less than \((m+k)/2.\) In particular, \(m(\phi)<(m+k)/2.\)
reviewed by: Lawrence Conlon
Mathematics Subject Classification ID: 57S20
Mathematics Subject Classification ID: 57R25
Mathematics Subject Classification ID: 57R30
zbMATH DE Number: 4098321
zbMATH Keywords: rank of manifold
zbMATH Keywords: \({\mathbb{R}}^ p\)-action
zbMATH Keywords: commuting, everywhere linearly independent vector fields
zbMATH Keywords: minimum orbit dimension
author: Pierre Molino
author: Francisco-Javier Turiel
MaRDI profile type: Publication
OpenAlex ID: W2356187603
description: scientific article; zbMATH DE number 4098321