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oaioai:doaj.org/article:ea4e0f718fe7467c87ceaecf2dea1e5a

Geodesic Equations on Diffeomorphism Groups

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Publication date
1 March 2008
Publisher
'SIGMA (Symmetry, Integrability and Geometry: Methods and Application)'
Doi

    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 $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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