Geodesic Equations on Diffeomorphism Groups
Differential Geometry
2008-04-25 v1
Abstract
We bring together those systems of hydrodynamical type that can be written as geodesic equations on diffeomorphism groups or on extensions of diffeomorphism groups with right invariant or metrics. We present their formal derivation starting from Euler's equation, the first order equation satisfied by the right logarithmic derivative of a geodesic in Lie groups with right invariant metrics.
Cite
@article{arxiv.0803.1678,
title = {Geodesic Equations on Diffeomorphism Groups},
author = {Cornelia Vizman},
journal= {arXiv preprint arXiv:0803.1678},
year = {2008}
}
Comments
This is a contribution to the Proc. of the Seventh International Conference ''Symmetry in Nonlinear Mathematical Physics'' (June 24-30, 2007, Kyiv, Ukraine), published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/