This article is cited in 27 papers

Geodesic Equations on Diffeomorphism Groups

Cornelia Vizman

Department of Mathematics, West University of Timişoara, Romania

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.

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

MSC: 58D05; 35Q35

Received: November 13, 2007; in final form March 1, 2008; Published online March 11, 2008

Language: English

DOI: 10.3842/SIGMA.2008.030

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ArXiv: 0803.1678