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arXiv · 0803.1678

Geodesic Equations on Diffeomorphism Groups

Cornelia Vizman
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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 $L^2$ 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.

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Cornelia Vizman. 2008-03-11. Geodesic Equations on Diffeomorphism Groups. https://doi.org/10.3842/sigma.2008.030

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