Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 4 (2008), 030, 22 pages      arXiv:0803.1678      https://doi.org/10.3842/SIGMA.2008.030
Contribution to the Proceedings of the Seventh International Conference Symmetry in Nonlinear Mathematical Physics

Geodesic Equations on Diffeomorphism Groups

Cornelia Vizman
Department of Mathematics, West University of Timisoara, Romania

Received November 13, 2007, in final form March 01, 2008; Published online March 11, 2008

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 L2 or H1 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.

Key words: Euler's equation; diffeomorphism group; group extension; geodesic equation.

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