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Geodesic flow on the diffeomorphism group of the circle

Constantin, Adrian LU and Kolev, B (2003) In Commentar II Mathematici Helvetici 78(4). p.787-804
Abstract
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.
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
geodesic flow, diffeomorphism group of the circle
in
Commentar II Mathematici Helvetici
volume
78
issue
4
pages
787 - 804
publisher
Birkhaüser
external identifiers
  • wos:000186461800008
  • scopus:0242350978
ISSN
1420-8946
DOI
language
English
LU publication?
yes
id
5608f155-bc97-48c1-a335-8bab6e12d7ca (old id 296299)
date added to LUP
2007-08-28 10:05:46
date last changed
2018-06-17 03:50:18
@article{5608f155-bc97-48c1-a335-8bab6e12d7ca,
  abstract     = {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.},
  author       = {Constantin, Adrian and Kolev, B},
  issn         = {1420-8946},
  keyword      = {geodesic flow,diffeomorphism group of the circle},
  language     = {eng},
  number       = {4},
  pages        = {787--804},
  publisher    = {Birkhaüser},
  series       = {Commentar II Mathematici Helvetici},
  title        = {Geodesic flow on the diffeomorphism group of the circle},
  url          = {http://dx.doi.org/},
  volume       = {78},
  year         = {2003},
}