TY - JOUR
T1 - Equations of Camassa-Holm type and the geometry of loop groups
AU - Górka, Przemysław
AU - Pons, Daniel J.
AU - Reyes, Enrique G.
N1 - Funding Information:
We thank Prof. V. Ovsienko for his kind interest in this work. E.G.R’s research has been partially supported by the FONDECYT grant #1111042 .
PY - 2015/1/1
Y1 - 2015/1/1
N2 - We recall some of Arnold's classical work on the Riemannian geometry of diffeomorphism groups, we provide easily computable formulae for the sectional curvature in the case of the diffeomorphism group of the circle, and we observe that this group has a CR-manifold structure. We also present examples of bona fide hamiltonian equations in infinitely many derivatives.
AB - We recall some of Arnold's classical work on the Riemannian geometry of diffeomorphism groups, we provide easily computable formulae for the sectional curvature in the case of the diffeomorphism group of the circle, and we observe that this group has a CR-manifold structure. We also present examples of bona fide hamiltonian equations in infinitely many derivatives.
KW - Camassa-Holm equation
KW - Diffeomorphism group
KW - Equations with infinitely many derivatives
KW - Euler equation on Lie groups
KW - Sectional curvature
UR - http://www.scopus.com/inward/record.url?scp=84912028252&partnerID=8YFLogxK
U2 - 10.1016/j.geomphys.2014.07.028
DO - 10.1016/j.geomphys.2014.07.028
M3 - Article
AN - SCOPUS:84912028252
SN - 0393-0440
VL - 87
SP - 190
EP - 197
JO - Journal of Geometry and Physics
JF - Journal of Geometry and Physics
ER -