We study the exponential maps induced by Sobolev type right-invariant (weak) Riemannian metrics of order k (greater or equal to 1) on the Lie group of smooth, orientation preserving diffeomorphisms of the circle. We prove that each of them defines an analytic Fréchet chart of the identity.
Classification :
22E65, 58B20, 17B68
Mots-clés :
Group of diffeomorphisms, Riemannian exponential map, Camassa-Holm equation
Affiliations des auteurs :
Thomas Kappeler
1
;
Enrique Loubet
1
;
Peter Topalov
2
1
Mathematisches Institut, Universitaet Zuerich, Winterthurerstrasse 190, 8057 Zuerich, Switzerland
2
Department of Mathematics, Northeastern University, 360 Huntington Avenue, Boston, MA 02115, U.S.A.
Thomas Kappeler; Enrique Loubet; Peter Topalov. Analyticity of Riemannian Exponential Maps on Diff(T). Journal of Lie Theory, Tome 17 (2007) no. 3, pp. 481-503. http://geodesic.mathdoc.fr/item/JOLT_2007_17_3_a2/
@article{JOLT_2007_17_3_a2,
author = {Thomas Kappeler and Enrique Loubet and Peter Topalov},
title = {Analyticity of {Riemannian} {Exponential} {Maps} on {Diff(T)}},
journal = {Journal of Lie Theory},
pages = {481--503},
year = {2007},
volume = {17},
number = {3},
url = {http://geodesic.mathdoc.fr/item/JOLT_2007_17_3_a2/}
}
TY - JOUR
AU - Thomas Kappeler
AU - Enrique Loubet
AU - Peter Topalov
TI - Analyticity of Riemannian Exponential Maps on Diff(T)
JO - Journal of Lie Theory
PY - 2007
SP - 481
EP - 503
VL - 17
IS - 3
UR - http://geodesic.mathdoc.fr/item/JOLT_2007_17_3_a2/
ID - JOLT_2007_17_3_a2
ER -
%0 Journal Article
%A Thomas Kappeler
%A Enrique Loubet
%A Peter Topalov
%T Analyticity of Riemannian Exponential Maps on Diff(T)
%J Journal of Lie Theory
%D 2007
%P 481-503
%V 17
%N 3
%U http://geodesic.mathdoc.fr/item/JOLT_2007_17_3_a2/
%F JOLT_2007_17_3_a2
