Geodesic flow on the diffeomorphism group of the circle
(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:
https://lup.lub.lu.se/record/296299
- author
- Constantin, Adrian LU and Kolev, B
- organization
- publishing date
- 2003
- 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
- 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
- 2024-09-11 07:35:29
@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}}, 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}}, }