Geodesic flow on the diffeomorphism group of the circle
type: Item
instance of: scholarly article
title: Geodesic flow on the diffeomorphism group of the circle
zbMATH Open document ID: 1037.37032
author: A. Constantin
author: B. Kolev
published in: Commentarii Mathematici Helvetici
publication date: 2004-02-05T00:00:00Z
review text: Summary: We show that certain right-invariant metrics endow the infinite-dimensional Lie group of all smooth orientation-preserving diffeomorphisms of the circle with a Riemannian structure. The study of the Riemannian exponential map allows us to prove infinite-dimensional counterparts of results from classical Riemannian geometry: The Riemannian exponential map is a smooth local diffeomorphism and the length-minimizing property of the geodesics holds.
Mathematics Subject Classification ID: 37K65
Mathematics Subject Classification ID: 35Q35
Mathematics Subject Classification ID: 58B25
Mathematics Subject Classification ID: 53D25
zbMATH DE Number: 2038409
zbMATH Keywords: geodesic flow
zbMATH Keywords: diffeomorphism group of the circle
zbMATH Keywords: inviscid Burgers equation
zbMATH Keywords: Camassa-Holm equation
Wikidata QID: Q58870065
MaRDI profile type: Publication
full work available at URL: s00014-003-0785-6
OpenAlex ID: W2087328884
DOI: 10.1007/S00014-003-0785-6
description: scientific article; zbMATH DE number 2038409