English

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 L2L^2 or H1H^1 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.

Keywords

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/

R2 v1 2026-06-21T10:20:42.060Z