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On geodesic exponential maps of the Virasoro group

Constantin, Adrian LU ; Kappeler, T.; Kolev, B. and Topalov, P. (2007) In Annals of Global Analysis and Geometry 31(2). p.155-180
Abstract
We study the geodesic exponential maps corresponding to Sobolev type right-invariant (weak) Riemannian metrics mu((k)) (k >= 0) on the Virasoro group Vir and show that for k >= 2, but not for k = 0, 1, each of them defines a smooth Frechet chart of the unital element e is an element of Vir. In particular, the geodesic exponential map corresponding to the Korteweg - de Vries (KdV) equation ( k = 0) is not a local diffeomorphism near the origin.
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
geodesic exponential maps, Virasoro group
in
Annals of Global Analysis and Geometry
volume
31
issue
2
pages
155 - 180
publisher
Springer
external identifiers
  • wos:000244190800003
  • scopus:33847253064
ISSN
1572-9060
DOI
10.1007/s10455-006-9042-8
language
English
LU publication?
yes
id
946e56f5-62f8-49fd-8a93-bba3482b8c66 (old id 674857)
date added to LUP
2007-12-06 10:53:59
date last changed
2017-08-20 04:29:38
@article{946e56f5-62f8-49fd-8a93-bba3482b8c66,
  abstract     = {We study the geodesic exponential maps corresponding to Sobolev type right-invariant (weak) Riemannian metrics mu((k)) (k >= 0) on the Virasoro group Vir and show that for k >= 2, but not for k = 0, 1, each of them defines a smooth Frechet chart of the unital element e is an element of Vir. In particular, the geodesic exponential map corresponding to the Korteweg - de Vries (KdV) equation ( k = 0) is not a local diffeomorphism near the origin.},
  author       = {Constantin, Adrian and Kappeler, T. and Kolev, B. and Topalov, P.},
  issn         = {1572-9060},
  keyword      = {geodesic exponential maps,Virasoro group},
  language     = {eng},
  number       = {2},
  pages        = {155--180},
  publisher    = {Springer},
  series       = {Annals of Global Analysis and Geometry},
  title        = {On geodesic exponential maps of the Virasoro group},
  url          = {http://dx.doi.org/10.1007/s10455-006-9042-8},
  volume       = {31},
  year         = {2007},
}