Geodesic Equations on Diffeomorphism Groups

Cornelia Vizman

Symmetry, integrability and geometry: methods and applications, Tome 4 (2008)

Résumé

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 $L^2$ or $H^1$ 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.

Détail

Keywords: Euler's equation; diffeomorphism group; group extension; geodesic equation.

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