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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
and
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
Birkhäuser Verlag
external identifiers
  • wos:000186461800008
  • scopus:0242350978
ISSN
1420-8946
DOI
10.1007/s00014-003-0785-6
language
English
LU publication?
yes
id
5608f155-bc97-48c1-a335-8bab6e12d7ca (old id 296299)
date added to LUP
2016-04-01 11:52:09
date last changed
2022-04-28 21:12:09
@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}},
  keywords     = {{geodesic flow; diffeomorphism group of the circle}},
  language     = {{eng}},
  number       = {{4}},
  pages        = {{787--804}},
  publisher    = {{Birkhäuser Verlag}},
  series       = {{Commentar II Mathematici Helvetici}},
  title        = {{Geodesic flow on the diffeomorphism group of the circle}},
  url          = {{http://dx.doi.org/10.1007/s00014-003-0785-6}},
  doi          = {{10.1007/s00014-003-0785-6}},
  volume       = {{78}},
  year         = {{2003}},
}