A note on the linearity of real-valued functions with respect to suitable metrics
type: Item
instance of: scholarly article
title: A note on the linearity of real-valued functions with respect to suitable metrics
zbMATH Open document ID: 1067.58011
author: Patrizio Frosini
published in: Geometriae Dedicata
publication date: 2005-03-15T00:00:00Z
review text: The author proves that for every real-valued Morse function \(f\) on a smooth manifold and every neighborhood \(U\) of its critical points, a suitable Riemannian metric exists such that \(f\) is linear outside \(U\). The proof, based on the notion of flow set, relies on vertical extension to the flow set.
Mathematics Subject Classification ID: 58E05
Mathematics Subject Classification ID: 53C20
Mathematics Subject Classification ID: 58C05
zbMATH DE Number: 2145811
zbMATH Keywords: linear functions
zbMATH Keywords: Riemannian metric
reviewed by: Marlène Frigon
MaRDI profile type: Publication
full work available at URL: s10711-004-8119-4
OpenAlex ID: W1989089408
cites work: Q5589856
cites work: Natural pseudodistances between closed manifolds
cites work: Morse theory of harmonic forms
cites work: Intrinsic harmonicily of Morse functions
cites work: A note on Morse theory of harmonic 1-forms
cites work: Q4320141
cites work: Q3952851
DOI: 10.1007/S10711-004-8119-4
description: scientific article; zbMATH DE number 2145811