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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
; ; and
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
2016-04-01 16:45:40
date last changed
2022-03-22 20:52:25
@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}},
  keywords     = {{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}},
  doi          = {{10.1007/s10455-006-9042-8}},
  volume       = {{31}},
  year         = {{2007}},
}